1997 ducati 748 wiring diagram - span class news dt nov 06 2018 span nbsp 0183 32 i have been offered a 748 loom but unsure if it is a direct replacement i have also spoken to a few panies specialising in electrical repairs but do not want to look at the loom off the bike so if anyone can confirm interchangeability of the 748 998 looms or mail me a 748 wiring diagram i would be most grateful span class news dt aug 08 2011 span nbsp 0183 32 ducati 748 916 service repair manual 1994 1997 eng ita ger fra esp by admin24 183 august 8 2011 download ducati 748 916 service repair manual 1994 1997 eng ita ger fra esp hundreds of illustrations wiring diagram showing plete procedures of disassembly and reassembly span class news dt jul 24 2014 span nbsp 0183 32 ducati 748 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 factory service repair manual pdf download download here you can find the most plete service and free ducati motorcycle.
service manuals for download lots of people charge for motorcycle service and workshop manuals online which is a bit cheeky i reckon as they are freely available all over the inter 163 5 each online or download your ducati manual here for free factory service repair manual ducati 748 916 year 1994 1997 covers the following ducati model 748 monoposto strada 748 sport production 748 biposto 916 monoposto strada 916 senna 916 sport production 916 biposto usually these motos changes only few through the years the manual works well similiar model year language eng ita ger fra esp format file ducati 748 electrical wiring diagram you search auto repair manual pdf ducati 748 electrical wiring diagram if there are search results will appear below if search results do highly detailed printable diagrams once you have found the information you require simply print it out and start the repair.
or take your laptop tablet to the vehicle home 187 motorbikes 187 ducati 187 748 187 ducati 748 916 service repair pdf manual 1997 2000 ducati 748 916 service repair pdf manual 1997 2000 ducati 748 916 service repair some ducati motorcycle manuals pdf wiring diagrams are above the page ducati pany was founded in 1926 in bologna the founders of the pany were the brothers adriano and marcello ducati both of them were interested in radio so the first focus of the pany s production was just radio engineering span class news dt oct 14 2013 span nbsp 0183 32 hi folks just wondering if anyone s got a wiring diagram for a 749 999 please bit of a long shot but i have a 748r that now has a 998s motor with 999 heads i ve bought the 999 coils that sit on top of the heads so i can do away with the clunky 748 99 coils but notice the 999 items have 3 wires yet the older ones only have two suzuki.
gsx1300r hayabusa repair manual 19992013 haynes 4184 suzuki gsx1300r hayabusa repair manual 19992013 1997 ducati 748 wiring diagram 1113sandybloomnl 2002 ducati 748 wiring diagram circuit diagram images rh x6 homeschoolingiscool co hayabusa wiringdiagram ducati 748 wiring diagram you search auto repair manual pdf ducati 748 wiring diagram if there are search results will appear below if search results do not exist please search by others keyword 1994 1997 eng ita ger fra esp factory service repair manual ducati 748 916 year 1994 1997 covers the following ducati model instant download ducati 748 916 service repair manual with illustrations wiring diagram and photos in pdf format ducati 748 916 service repair manual download de en it es fr this is the most diagrams specifications span class news dt nov 27 2013 span nbsp 0183 32 regulator rectifier for ducati cagiva laverda 350ss 400ss.
Ducati 748 916 996 998 swing arm bearings pair high quality ducati 748 wiring diagram.
1997 ducati 748 wiring diagram #12.
2002 ducati 748 wiring diagram auto electrical wiring diagram u2022 rh focusnews co at ducati front wiring harness late style 748 996 superbike 748 748s rh.


The U.S. Food and Drug Administration (FDA) announced Friday that it is banning the sale of pure and bulk caffeine products after 2 young men died from an accidental overdose.
Dietary supplements that contain pure or highly concentrated caffeine in powder or liquid forms "present a significant public health threat," FDA said in a Public Health Alert.
Free Confidential Lawsuit Evaluation: If you or a loved one suffered a caffeine overdose, you should contact our law firm immediately. You may be entitled to compensation by filing a suit and our lawyers can help.
April 16, 2018 – A half cup of a highly concentrated liquid caffeine can have about 2,000 mg of caffeine, but a single teaspoon of bulk powdered product can have more than 3,000 mg, equal to 20 to 28 cups of coffee, which is a fatal dose.
The caffeine supplements can no longer legally be sold in bulk quantities directly to consumers, FDA said.
"Regardless of whether the product contains a warning label, such products present a significant and unreasonable risk of illness or injury to the consumer," FDA said.
In 2015 and 2016, FDA issued warning letters to at least 5 sellers of powdered caffeine in an attempt to stop the supplements from being marketed in the U.S. However, these actions had little effect.
"Despite multiple actions against these products in the past, we've seen a continued trend of products containing highly concentrated or pure caffeine being marketed directly to consumers as dietary supplements and sold in bulk quantities, with up to thousands of recommended servings per container," said FDA Commissioner Scott Gottlieb, M.D.
Do I Have a Caffeine Overdose Lawsuit?
The Pharmaceutical Litigation Group at our law firm is an experienced team of trial lawyers that focus on the representation of plaintiffs in caffeine overdose lawsuits. We are handling individual litigation nationwide and currently accepting new injury and death cases in all 50 states.
Free Confidential Evaluation: Again, if you or a loved one was injured by a caffeine overdose, you should contact our law firm immediately. You may be entitled to a settlement by filing a suit and we can help.


Look through the profiles of Member members here at Maryland Chat City that are tagged with Blonde. Dating others that have like minded interests is a pefect way to come up with ideas to do once you are dating. Register for a Totally Free Profile to Go out Today!
To message any member on Maryland Chat City, you need to create a 100% Free Account to ensure you are who you say you are. After you have proven you are scammer, you can start contacting to find out if they like your profile. It's very simple to find just about anyone. All you have to do is send a wink or quick message and wait for for them to get back to you. Once there is a common interest, you can meet up to find out if there is a genuine connection. So what are you waiting for? Open up a free account today!


text:
Musicians from Hiroshima and five nuclear powers hold concert for peace
by Aya Kano, Staff Writer
The "Concert for Peace in Hiroshima," which featured musicians from Hiroshima and five nuclear weapon states performing together at Aster Plaza, in downtown Hiroshima, was held on April 1. The event reunited musicians who had staged a concert in New York in connection with the 2010 Nuclear Non-proliferation Treaty (NPT) Review Conference. About 430 people attended the concert, designed to appeal for the abolition of nuclear weapons.
Thirty-two musicians from the United States, Russia, France, the United Kingdom, and China joined about 130 people from Hiroshima, including members of a choir. The program included piano and violin pieces, arias, and other performances. A British actress recited an English version of the A-bomb poem "Umashimenkana" ("We Shall Bring Forth New Life").
To close the concert, everyone at the venue sang the well-known Japanese song "Furusato" ("Hometown"). Kana Takeyama, 18, a university student who lives in Nishi Ward, Hiroshima, remarked, "Music has the power to unite people's ideas across national borders."
The New York concert was spearheaded by Yasuko Mitsui, a harpsichord player and resident of Hatsukaichi, Hiroshima Prefecture who called on musicians from the five countries to participate. Those who took part in New York hoped to stage another concert in Hiroshima, and the executive committee, chaired by Kazutaka Yamamoto, organized the Hiroshima event.
(Originally published on April 2, 2013)

redpajama_set_name: RedPajamaCommonCrawl


Scoliosis is a lateral and rotational misalignment of the spine of more than 10º as seen on x-rays. It must not be confused with bad posture.
The spine when misaligns causes head, shoulders and hip tilt and apparent leg length inequality.


text:
Intermediary and Wealth
Corporate Trustee Services
Who we invest for
What we invest in
Policies and business principles
M&G online
Your investment choices
Make an investment
Consider the risk
Fixed income (bonds)
Choose your investment
Tax-efficient investing
Child Trust Fund transfers
Get financial advice
Funds by asset class
Fund charges
Fund charge calculator
Top up your investment with a lump sum
Amend a Direct Debit
Transfer an ISA or Junior ISA to M&G
Transfer a Child Trust Fund (CTF) to M&G
Switch between M&G products and funds
Withdrawing your M&G investment
Managing an investment by proxy
Half-yearly statement mailing
M&G Guides
ISA investing explained
Forms and literature
Key Investor Information Documents (KIIDs)
The information in this site is intended for financial advisers only.
The information contained in these pages must not be used or relied upon by private investors. We recommend that you read our 'Terms & Conditions' before browsing the site.
Please click the appropriate button to the right to confirm that you are a financial adviser and wish to continue.
A cookie is a small piece of information generated by a web server and sent to your computer when you access this website. Our cookies do not hold any personal information about you. This cookie is used to remember your selection next time you visit our site. It is stored on your computer's hard drive but can be deleted at any time via the 'Tools' option on your internet browser. By clicking to accept and proceeding beyond this page, you agree to accept this cookie from this site.
This site also uses other types of cookies. For more details see our Privacy & Cookies policy. This provides options of how to opt out of these cookies.
I confirm that I am an end investor
I am not an end investor
Please choose your audience type: Charities Corporate Trustee Services Institutional Intermediary and Wealth Private Investors
Global Dividend Fund
Sterling A Inc
M&G Global Dividend Fund
Objective and risks
M&G Global Dividend Fund - Sterling A Inc - Factsheet (UK) PDF
M&G Global Dividend Fund - GBP - A Inc - Costs and charges illustration PDF
M&G Global Dividend Fund - GBP - A Inc - Key Investor Information Document (UK) PDF
M&G Global Dividend Fund - Interim Long Report PDF
M&G Global Dividend Fund - Interim Short Report PDF
M&G Global Dividend Fund - Annual Long Report PDF
M&G Global Dividend Fund - Annual Short Report PDF
M&G Global Dividend Fund - Instrument of incorporation PDF
M&G Global Dividend Fund - Prospectus PDF
Stuart Rhodes
Fund manager tenure from 18/07/2008
Stuart Rhodes has been the manager of the M&G Global Dividend Fund since its launch in July 2008 and the manager of the Luxembourg-domiciled M&G (Lux) Global Dividend Fund since its launch in December 2018. He was appointed deputy manager of the M&G North American Dividend Fund in April 2015, of the M&G (Lux) North American Dividend Fund in November 2018 and of the M&G Global Themes Fund in January 2019. Stuart joined M&G in 2004 as a global equity analyst after graduating from Bath University with a degree in business administration. He is a CFA charterholder.
John Weavers
Deputy Fund Manager
John Weavers has been the fund manager of the M&G North American Dividend Fund since April 2015. In January 2016, he was appointed deputy fund manager of the M&G Global Dividend Fund, and has been the deputy fund manager for the M&G Global Listed Infrastructure Fund since the fund was launched in October 2017. Prior to April 2015, John was deputy fund manager of the M&G Pan European Dividend Fund and the M&G Dividend Fund for two years. John joined M&G as a graduate in 2007 and worked as an analyst in the Equity Research team before joining the Income team in January 2012. He graduated from Oxford University with an honours degree in politics, philosophy and economics and is a CFA charterholder.
Alex Araujo
Alex Araujo has been the manager of the M&G Global Listed Infrastructure Fund since it launched in October 2017, and was appointed manager of the M&G Global Themes Fund in January 2019. Alex initially joined M&G's income team in July 2015 and became co-deputy manager of the M&G Global Dividend Fund in April 2016. Alex has 25 years of experience in financial markets, having previously worked at UBS and BMO Financial Group. He graduated from the University of Toronto with an MA in economics and is a CFA charterholder.
Kotaro Miyata
Investment Specialist
Kotaro Miyata is the investment specialist providing support for M&G's equity income fund range which includes the M&G Global Dividend Fund, as well as the M&G Global Listed Infrastructure Fund and the M&G (Lux) Global Listed Infrastructure Fund which were launched in October 2017. Prior to joining M&G in 2006, he was a fund manager at Invesco Asset Management, where he was responsible for European and UK equities within the Global Equities team. Kotaro holds the Securities Institute Diploma and graduated from Oxford University in 1994 with a degree in classics.
By telephone
Call our Investment Helpline on 0800 389 8600* from 8.00am to 6.00pm Monday to Friday and 9.00am to 1.00pm on Saturday to make an investment.
Remember to have your M&G Client Reference to hand if you're already an M&G customer. Failure to provide this may affect your ability to invest with us. You'll also need your debit card and, if you're opening a new product, your National Insurance Number.
*All calls are free within the UK. For your security and to improve the quality of our service we may record and monitor calls.
Send your application form to us at:
M&G Customer Relations,
The M&G Group
CM99 2XG
Download an application form here
Security and financial crime
The value of the fund's assets will go down as well as up. This will cause the value of your investment to fall as well as rise and you may get back less than you originally invested.


text:
5. Promote Educational Excellence (32% of surveyed members)
Basic Principle: Although differences remain as to what reforms to support, republicans are committed to educational excellence in support of the goal of leaving no child behind. Our public education system is not producing results. Our youth "feel" more competent but consistently perform at low levels of achievement compared to other industrial countries. A strong education system that works is very important to the future of our country. Ignorance is dangerous not only to our children but to our way of life.
"We can rally around Education reform. Better teachers (more incentive-pay and accountability), a more comprehensive curriculum and a broader scope of evaluating student achievement." Billy Cornett
"Accountability in Education means setting standards to leave no child behind." Judy Biviano Lloyd, Bay Area Regional Chair, Bush-Cheney 2000
"Local people should have more control over how their children are to be educated. We have to trust parents as to what is best for their children." James E Mertzel DDS
"The voucher issue is quite divisive and does not play well with the general public. However, the issue can be approached by first promoting a voucher concept within the public system--that is, to allow parents to enroll their children in any public school that meets their students' needs. That concept is common in the higher education realm but not in K-12. Why not? The faculty in higher education has unions, too, but they also have to compete for customers, and the customers (students) direct where the public dollars go." Karin Dowdy
"RETURN CONTROL TO LOCAL LEVEL AND EVENTUALLY SCHOOL CHOICE FOR PARENTS: The school system has been a complete disaster, and the children are the victims. The attempt to standardize education at the State level so that all children would receive the same level of education, no matter rich or poor, black or white, has led to a lower standard for schools that excelled while not helping those for whom the reforms were made. More than that, it has led to unreasonable power for the California Teachers Association. The leaders of CTA are, for the most part, not teachers, but use their name and power to speak in their name. Again, this has not been for the benefit of students, nor even for the teachers on the front lines. These leaders' cushy jobs are at stake, and they lean on and support the Democratic Party to keep them. Returning local control to the schools would help School Boards meet the needs of their own students, not meet mandates that eat up valuable resources like time, money and endless reams of paper." Rosemary Loven, Director, Region I, Central Division, California Federation of Republican Women
"Education - Stay away from School vouchers (do not feel we have the votes to get that passed), but push for more charter schools. They are proving to be a success." Tony Dart, Santa Maria, Santa Barbara County
Return to main survey page.
United We Can Win!
Email: info@unitedwecanwin.com
© 2002 - 2012 Dr. Terry Paulson. All Rights Reserved.


In Missouri, the compensation that you receive in a car or truck accident caused by another driver is determined in part by the amount of the medical bills charged by your providers. As a result of a recent case handed down by the Missouri Supreme Court, juries may be informed of at least two numbers regarding the medical bills.
For example, if your medical bills were paid by your health insurance, the insurance company may get to inform the jury that this amount of the medical bills has been paid. In some cases, the amount of bills paid does not affect the recovery due to the nature of the injuries. However, in cases, where the injuries are thankfully not as severe the amount of medical bills can have an important consideration to the amount of the recovery.
Issues such as the value of the medical bills in personal injury cases are extremely important in determining your compensation for a car accident. An experienced personal injury attorney will be able to obtain evidence that establishes the amount of medical bills charged by the health care providers is the proper amount for the jury to consider. Under the law, this evidence must be obtained outside the request for records.
When an insurance company tells you that it will only consider the amount paid, contact a car accident Mike Sudekum attorney for more information.


XtremeSystems Forums > Hardware > Macintosh & Others > Fastest Macintel in the world!!
View Full Version : Fastest Macintel in the world!!
thats pretty pimp. More info on it plz!
How did you OC it?
On that note, I think that the Mac Pro would own it in apps like FCP and Logic.
I'm not so sure. Not many programs take full advantage of the four cores yet, and with that overclock and less core overhead, that would be a pretty quick mac.
In this fcp rendering benchmark, the Mac Pro was just as fast with two of its cores disabled.
On the other hand with the Pro, you could render and use the other two cores to encode.
How well does the hackintosh work?
Damn my MacBook only scores 71.14 on CPU.
XEON 5080 (3.73Ghz) enabled Mac Pro.
it's easy to use mac & windows in same pc?


TUCSON, Ariz., Dec. 6, 2017 /PRNewswire/ -- Raytheon Company's (NYSE: RTN) Missile Systems business received its sixth consecutive superior security rating from the Defense Security Service. Missile Systems achieved a score of 851, just 14 points shy of perfect. DSS awarded the score and rating after a week-long audit of the Tucson, Arizona, plant site.
"Raytheon's commitment to national security is unwavering," said Dr. Taylor W. Lawrence, Raytheon Missile Systems president. "Everyone here understands the imperative to protect customer information. This superior rating validates all of our hard work and dedication."
Supporting national security and the military, DSS is responsible for approximately 13,000 cleared contractor facilities. The agency ensures the security of the nation's technological base and oversees the protection of U.S. and foreign classified information in industry. Fewer than four percent of the facilities DSS oversees receive a superior rating.
"Raytheon Missile Systems continues to strive for security excellence and has been extremely proactive in integrating the risk-focused approach into every facet of their industrial security program," said Leslie Whitaker, Industrial Security representative at DSS.


I've never been much of a sporty person... always hated team sports. I could never get into stuff like baseball, hockey, or anything team related. That goes for both watching and playing sports. I was more of a jazz and tap kind of dancer, a swimmer, and a skater. The last couple years or so I started getting into yoga. I've never been one for the gym and was quite shy when it came to joining a class. I did however, join a yoga class at one point, but found I was more comfortable in doing yoga at home. Being new to it, there were quite a number of moves that I tried... the helpful part of being in a class, is to have someone help you with your poses.
If you're someone who's somewhat shy like me, and would like to learn about yoga and all the different poses available... you could take a look at the book: Just Do Yoga! It's a complete guide to yoga with all the different poses for total mind and body bliss. I've read the book a few times already, and it's a very easy read. I've accomplished a third of the poses, with two thirds to still try.
Would I recommend this book? Sure... the only thing that I would suggest to the creator (Julie Schoen), is to create the book with a ring type binding, so that you can follow the pages while you're actually doing the yoga. Currently with the way that the book is constructed, it's difficult to hold it open while trying different poses. Other than that, it's an awesome book.
Interested in getting a copy today? Of course you are... click here!


Wendy Christy, the Children's Librarian at the Saline County Public Library, shared with me that her library has decided to ditch the nationwide summer programming, and is going with the theme Libraries Are For Everyone! I mean, WOW!!!
She didn't write to me to just tell me that, but to also request a set of signs in Marshallese to reflect this group in their community. Fortunately, she used her awesome networking skills and found a translation through the fab Erin Renollet. As an FYI this translates literally to libraries are for the public and for everyone.
Thank you both Wendy and Erin, for both caring and sharing!!!!!


text:
Bitch : A Revolutionary Guide to Sex, Evolution and the Female Animal
Yayınevi: Doubleday
Mother. Daughter. Ruler. Provider. What does it mean to be female?
The female species has never been more scrutinized or politicised. As we search to define our gender, combat prejudice, and celebrate the myriad of femininity - what can the animal kingdom teach us about its true nature?
In BITCH, award winning zoologist, broadcaster and author Lucy Cooke, takes the reader on a global journey to meet the animals and scientists that are helping to redefine female species and release it from the shackles of stereotype.
Lucy will present us with a dazzling portrait of the female, introducing us to polyamorous chimps, alpha-female hyenas, menopausal killer whales and lesbian lizards. By showing us the spectrum of the species, she sets out to re-write the evolutionary labels that have come to define a gender and propose a new understanding of what it means to be female today.


The theme you requested should be fun.
How would you define and control the dictator?
I'd imagine we'd have to enforce it through staff.
RE: Char reset on own server ?
Open up your servers users.eco file with Winrar (or 7zip) and delete your file inside.
Doing this though will keep your buildings in a semi glitchy state. So this method is only useful if you want to want to reset your stats and inventory.
A little more info about the issue and if you want to try to fix it.
[Server Bug] An item with the same key has already been added.
The error itself can be found in several users in your server, it seems one user is not capable of having "Same key" issues. This means that at least two users in your server are causing this bug. I have not gone as far as figuring out what that specific key is, due to my sanity not allowing it.
Open the "Users.eco" file with Winrar (probably 7Zip) and essentially you will have to start culling the population until the server no longer throws the error. From there you add users back and attempt to mark who or what creates a new issue.
After this I mix and matched to see if any of these faulty key users could be in the server together. (Who knows, maybe there are several different duplicate keys) So you spend time testing that too.
At this point you can delete all the faulty users or keep 1 faulty user standing (you will have to delete next server restart though, don't know why, but its a thing). Your server will run fine again, the deleted players will however all have lost their inventory.. And deeds unless they were put in a chest.
I've been forced to wipe the server several times at dismay of the players. It is inherently impossible to actually run a semi populated server due to this issue. It's crazy... Final note is that obviously due to the nature of the bug, you will likely end up doing this EVERY SINGLE TIME reboots or crashes. Have fun!
One last edit, obviously.. I cannot recommend deleting player files, as I have no clue how they are linked with for example world objects. So you might just create bigger issues down the road, I for myself really wanted to keep this world going so this is the path i took.
Players who got their files deleted can no longer use /reopen, they can however use their building as if it was theirs.
Added the shop and setup the first line of base prices.
Stock will be limited, however our initial focus is to attempt to drain gold and copper from the world to get coins created.
Updated to Alpha 0.2! :) Time for testing!
I would like to apply for a spot.
Added you to the white list in case we lock it up.
Could you expand on your theme? At what rate would you like to see em lengthened?
We as group would like to challenge the community in several new environments. We believe that Eco will be an amazing playground for several social and game play experiments. So beyond the normal game play we would love to add a twist every week/month depending on Meteor cycle.
It would be amazing to see more animals/mineral being mined due to currency value, can we make coins have a specific effect on the ecosystem? Or better yet, will we see people specialize to gain the most income from their profession?
We will setup a town hall to mint and a shop that accepts coins.
We will start at a standard, but slowly increase or decrease the value of items depending on purchases.
Teleport command to Mint and Shop will be available.
Laws can be enacted and will be voted on, will your lust for currency change things?
Currently we are also looking for staff to assist in our projects. Are you willing to help us develop and create a better server experience for everyone? Send me a message on these forums or worldofeco.net/forum .
Currently the server is running Alpha 0.1 on a clean world. :) You can try out your connection with our server and see if it works out for you.
No abuse of glitches within the alpha software (dupes etc) Please report these to staff.
Attempt to assist with the theme, if you just want to play Eco you are welcome to do so. But do not actively interfere with the testing.


text:
\section{Introduction}
One of the most distinctive features of the quantum field theory is the existence of quantum vacuum fluctuations that have no counterpart in the classical physics. Generation of real particles out of the quantum vacuum fluctuations, or dynamical vacuum amplification, is one of the manifestations of such fluctuations on the macroscopic level.
Examples of the quantum vacuum amplification phenomenon include the \textit{Schwinger} effect \cite{Schwinger}, which is the electron-positron pair production from the vacuum under the action of strong electric fields;
\textit{Hawking} radiation \cite{Hawking}, which results from a vacuum instability of quantum fields at a black-hole horizon;
the \textit{Unruh} effect \cite{Unruh}, which predicts that an accelerating observer traveling through the Minkowski vacuum will observe a thermal spectrum of particle excitations;
and the \textit{dynamical} Casimir effect (DCE) which concerns the generation of real particles (conventionally creation of photons) out of the quantum vacuum \cite{Yablonovitch,Schwinger2,Wilson} when the boundary conditions of the field are varied at a fast-enough rate\cite{Moore,Davies,Dodonov1,Nation}.

In spite of the \textit{static} Casimir effect which results from a mismatch of vacuum modes in the space domain, the DCE arises from a mismatch of vacuum modes in the time domain.
The DCE can be explained qualitatively as a particular kind of the parametric amplification of quantum vacuum fluctuations in systems with time-dependent parameters leading to photon generation.
In addition to the theoretical investigations on the issue of particle generation via the DCE in a large variety of systems, ranging from cosmology to non-stationary cavity QED \cite{Daviesbook.Dodonov2.Dalvit.Dodonov3.Crocce.Dodonov4.Dodonov5}, various theoretical schemes for practical applications of the DCE have been suggested, including generation of photons with nonclassical properties \cite{Dodonov6,Dodonov7,Johansson}, generation of atomic squeezed sates \cite{Bhattacherjee}, generation of multipartite entanglement in cavity networks \cite{Felicetti}, and generation of EPR quantum steering and Gaussian interferometric power \cite{Sabin}.

Most of the schemes proposed until now to realize the DCE can be roughly separated into two categories: (a) the schemes based on the real mechanical motion of boundaries, e.g., mirrors of a cavity, a mechanism referred to as  motion-induced DCE (MIDCE) in the literature \cite{Barton}; and (b) the schemes based on the parametric amplification of vacuum fluctuations in media without moving boundaries, a process which is a kind of imitation of boundary motion and  known as parametric DCE (PDCE) \cite{DodonovPDCE}.

From the experimental point of view, in order to generate a measurable flux of real photons from vacuum, the real moving boundaries should oscillate at very high frequencies. Indeed, the resonance condition for realization of the MIDCE requires the mechanical frequency to be at least twice that of the cavity which still remains a serious problem.
Recently a high mechanical frequency as large as $ \omega_m/2\pi \sim 6 $GHz has been reported \cite{high mechanical frequency}. However, for the generation of Casimir radiation at the frequency of about $ \omega_c/2\pi = 5 $GHz a still higher mechanical frequency is needed. Consequently, alternative schemes based on imitation of boundary motions (PDCE) have been proposed. Some examples include periodic modulation of the optical properties of the boundary \cite{Lombardi,Dodonov8,Dodonov9} or of the optical path length of a cavity \cite{Dezael,Faccio,Motazedifard DCE}, and enhancing Casimir photon generation in a cavity within the driven Rabi model of the qubit-field interaction with a time-dependent modulation \cite{Hoeb}.
Some other experimental schemes aiming to observe the DCE can be found in \cite{Lombardi,Agnesi,Kawakubo}. Recently, the DCE has been realized experimentally in superconducting circuit QED through fast-modulating either the electrical boundary condition of a transmission line \cite{Pourkabirian} or the effective speed of light in a Josephson metamaterial \cite{Lahteenmaki}.

Besides, the MIDCE or PDCE proposals include analog models for generation of other particles than photons mostly in the physical systems including Bose-Einstein condensates (BECs). For example, the DCE of phonons in a time modulated atomic BEC \cite{Recati,Jaskula}, dynamical Casimir emission of Bogoliubov excitations in an exciton-polariton condensate suddenly generated by an ultrashort laser pulse \cite{Koghee}, phononic DCE in a time-modulated quantum fluid of light \cite{Busch}, DCE of magnon excitation in a spinor BEC driven by a time-dependent magnetic field \cite{Saito}, and the DCE of phonons in a gas of laser-cooled atoms with time-dependent effective charge \cite{Dodonov10} have been studied.

Over the past decade, we have witnessed remarkable and rapid progress in the field of cavity quantum optomechanics and it is currently subject to intense research investigations (for a recent review, see, e.g., \cite{Aspelmeyer}).
Optomechanical systems in which the electromagnetic radiation pressure is linearly or quadratically coupled to a mechanical oscillator (MO) have been widely employed in a large variety of applications; for example displacement and force sensing \cite{xsensing1,CQNCPRL,CQNCPRX,CQNCmeystre,CQNCmaximilian,aliNJP,complexCQNC}, ground-state cooling of the vibrational modes of an MO \cite{ground state cooling, Sideband cooling,Laser cooling,Teufel,Chan}, generation of entanglement \cite{Palomaki2,Paternostro,genes-entangelment}, synchronization of MOs \cite{Mari1,MianZhang,Bagheri,Shlomi,grebogi,foroud} and generation of nonclassical states of the mechanical and optical modes \cite{Borkje,Hammerer}. Furthermore, hybrid optomechanical systems consisting of atomic BECs have attracted considerable attention on studies such as nonlinear effects of atomic collisions on the optomechanical properties of a BEC trapped inside an optical cavity \cite{dalafi1}, control of optical bistability, cooling and entanglement using nonlinear atom-atom interaction \cite{dalafi2}, effects of the phase noise of the driving laser on the bipartire entanglement in a BEC-hybridized optomechanical cavity  \cite{dalafi3}, and also the effects of intrinsic cross-Kerr nonlinearity of an atomic BEC inside an optical cavity on the steady-state behavior of the system \cite{dalafi4}.

Nevertheless to our knowledge, there are only few recent investigations regarding the occurrence of DCE in optomechanical systems. Among them, we can mention Ref. \cite{Salvatore} as an MIDCE proposal in which it has been shown that a considerable number of photons  can be generated out of the vacuum for mechanical frequencies equal to or lower than the cavity-mode frequencies in the strong coupling regime without any time-dependent modulation. However, it is hardly achievable in the current technologies and it seems still to be far fetch.
Furthermore, two theoretical schemes have been proposed to realize the PDCE in cavity optomechanical systems in which the quantum vacuum is parametrically amplified by using external modulation techniques: the scheme of realizing the DCE in a non-stationary quantum well-assisted hybrid optomechanical cavity driven by an amplitude-modulated external laser pump \cite{Mahajan}, and the scheme for the realization of the DCE of phonon excitation in the so-called membrane-in-the-middle optomechanical system \cite{Thompson} which is pumped by a far-detuned driving classical laser and also is precooled down to almost the ground state by an auxiliary cavity mode \cite{motazedi2}.

Motivated by the above-mentioned interesting features of hybrid optomechanical systems in the field of DCE, in this paper we propose a theoretical scheme for controllable generation of the Casimir photons and phonons in an optomechanical cavity with a moving end mirror containing an interacting cigar-shaped BEC. Here, to achieve parametric amplification of quantum vacuum fluctuations, we consider an external time modulation on the spring coefficient of the MO which will be shown to be directly responsible for the amplification of the mechanical vacuum fluctuations of the MO, and indirectly responsible for the amplification of the atomic vacuum fluctuations of the BEC. In addition, by considering the time modulation of the two-body atomic collisions frequency we will show that it not only causes directly the amplification of the atomic vacuum fluctuations, but also indirectly induces the amplification of the mechanical vacuum fluctuations of the MO.
These two types of modulations can lead to the controllable generation of the mechanical- and Bogoliubov-type Casimir phonons in the steady-state.

 Moreover, in the regime of largely different optomechanical coupling strengths of the cavity field to the BEC and the MO corresponding to the \textit{coherent} regime a considerable number of Casimir photons can be generated due to the induced amplification of quantum vacuum fluctuations when the cavity is driven by a red-detuned laser. Furthermore, by analyzing the quantum Langevin equations (QLEs) in the Fourier space, we identify an induced frequency-dependent amplification coefficient which is analogous to the frequency-dependent amplitude in an optical parametric amplifier (OPA) and also is controllable via the parameters of the external modulations as well as cooprativities.

The paper is organized as follows. In Sec. \ref{sec2}, we describe the physical model of the system under consideration and illustrate the modulation scenarios together with their corresponding parametric amplification-type Hamiltonians.
In Sec. \ref{sec3}, the QLEs are derived and linearized around the semiclassical steady state, and in Sec. \ref{sec4} by solving the QLEs in the frequency space we find the self-energies and induced parametric amplifications of the photonic and phononic quantum vacuum fluctuations. In Sec. \ref{sec5}, we determined the steady-state mean number of generated Casimir photons and phonons in different regimes by solving the Lyapunov equation numerically. Finally, our conclusions and outlooks are summarized in Sec. \ref{sec6}.

\section{THEORETICAL DESCRIPTION OF THE SYSTEM}\label{sec2}

\begin{figure}
	\includegraphics[width=8.5cm]{1.pdf}
	\caption{(Color online) Schematic diagram of a BEC-hybridized driven optomechanical cavity with a movable end mirror whose spring coefficient, $ k(t) $, is modulated parametrically. It is also assumed that the two-body \textit{s}-wave scattering frequency of atomic collision, $ \omega_{sw}(t) $, is parametrically modulated. Both the moving mirror and the BEC interact with the single mode of the cavity in the red-detuned regime, although there is no direct interaction between the BEC and the mirror. The coherent modulations lead to the generation of Casimir photons and phonons which are controllable via the optomechanical and modulation parameters.}
	\label{fig1}
\end{figure}
As shown in Fig. (\ref{fig1}), we consider a driven \textit{hybrid} optomechanical cavity with lenghth $ L $ whose end mirror is free to oscillate at mechanical frequency  $ \omega_m $ .The cavity contains a cigar-shaped BEC of $ N $ ultracold two-level atoms with mass $ m_a $ and transition frequency $ \omega_a $. The cavity is driven at rate $E_L= \sqrt{\kappa P_L / \hbar \omega_L}$ through the fixed mirror by a laser with frequency $\omega_{L}$ and wavenumber $k_{0}=\omega_{L}/c$ ($P_{L}$ is the laser power and $\kappa$ is the cavity decay rate). The total many-body Hamiltonian of the system is given by

\begin{eqnarray} \label{H1total}
&& \hat H= \hat H_{cav}+ \hat H_{m}+ \hat H_{opt} + \hat H_{mod} + \hat H_{BEC}.
\end{eqnarray}
The first three terms in Eq. (\ref{H1total}) describe, respectively, the driven cavity field, the free mechanical resonator, and the optomechanical interaction which in the frame rotating at the driving laser frequency $ \omega_L $ can be written as
\begin{subequations}\label{H_c,m,opt}
\begin{eqnarray}
&& \hat H_{cav}=\hbar \Delta_c \hat a^\dag \hat a + i\hbar E_L (\hat a^\dag - \hat a), \\
&& \hat H_m=\frac{\hat p^2}{2m} + \frac{1}{2} m \omega_m^2 x^2 =\hbar \omega_m \hat b^\dag \hat b, \\
&& \hat H_{opt}= -\hbar g_0 \hat a^\dag \hat a (\hat b + \hat b^\dag),
\end{eqnarray}
\end{subequations}
where $ \hat a $ ($ \hat b $) is the annihilation operator of the cavity (mechanical) mode and $ \Delta_c= \omega_c-\omega_L $ is the detuning of the cavity mode from the driving laser frequency. Here, we have modeled the mirror as a single-mode MO of intrinsic frequency $ \omega_m $, effective mass $ m $, and damping rate $ \gamma_m $. The canonical position and momentum of the MO are $ \hat x= x_{zp}(\hat b + \hat b^\dag) $ and $ \hat p= \hbar (\hat b - \hat b^\dag)/2ix_{zp} $, respectively, with $ x_{zp}= \sqrt{\hbar / 2m\omega_m} $ being the zero-point position fluctuation. $ g_0=x_{zp} \omega_c /L $ stands for the single-photon optomechanical coupling.
The single-mode approximation for the mechanical and optical fields is an appropriate simplification provided that the cavity free spectral range is much larger than the mechanical frequency \cite{singlecavitymode} and the detection bandwidth is chosen such that it includes only a single isolated mechanical resonance and mode-mode coupling is negligible \cite{singlemechanicalmode}. The last two terms in Eq. (\ref{H1total}) describe, respectively, the time modulation of the spring coefficient of the MO and the Hamiltonian of the atomic BEC whose explicit forms will be determined in the following.

\subsection{Modulation of the mechanical spring coefficient}
We assume that the MO is parametrically driven by modulating its spring coefficient at twice its natural frequency, i.e., $k(t)= k+\delta k \cos(2\omega_{m} t +\varphi_m) $ ($ \varphi_m $ being the phase of external modulation) which is equivalent to the modulation of the mechanical frequency [ see Fig. (\ref{fig1})]. In this way, the Hamiltonian of the MO can be written as \cite{optomechanics with two phonon driving}
\begin{eqnarray} \label{H_m(t)}
&& \hat H_m(t)=\frac{ \hat p^2}{2m} + \frac{1}{2} k(t) x^2=\hat H_m + \hat H_{mod},
\end{eqnarray}
where
\begin{eqnarray} \label{H_mod(t)}
&& \hat H_{mod}(t)= \frac{1}{2} \delta k \cos(2\omega_m t) x^2.
\end{eqnarray}
Now, using the rotating wave approximation (RWA) over time scales longer than $ \omega_m^{-1} $ to ignore the fast rotating term in the shifted frequency of the MO, i.e., the term proportional to $\cos(2\omega_{m} t) \hat b^\dag \hat b $, the Hamiltonian of Eq. (\ref{H_mod(t)}) can be simplified as
\begin{eqnarray} \label{H_mod}
&& \hat H_{mod}(t)= \frac{i \hbar}{2} (\lambda_m \hat b^{\dag 2}  e^{-2i\omega_m t}- \lambda_m^\ast \hat b^2 e^{2i\omega_m t}),
\end{eqnarray}
where $ \lambda_m= \vert \lambda_m \vert e^{i\varphi_m} $ with $ \vert \lambda_m \vert= \delta k x_{zp}^2 / 2\hbar $.
The Hamiltonian of Eq. (\ref{H_mod}) describes the mechanical phonon analog of the degenerate parametric amplification (DPA) where the vibrational fluctuation of the MO plays the role of the signal mode in the DPA. Accordingly, it is expected that the coherent modulation of the mechanical spring coefficient or mechanical frequency leads to the amplification of quantum vacuum fluctuations of the MO, i.e., dynamical Casimir emission of mechanical phonons (mechanical-type Casimir phonons). Note that by fixing the phase of modulation $ \varphi_m $, it is always possible to take $ \lambda_m $ as a real number.

\subsection{Second quantized Hamiltonian of the BEC}
We now assume $ N $ ultracold two-level atoms of the BEC to be confined in a cylindrically symmetric optical trap with a transverse trapping frequency $ \omega_\bot $ and negligible longitudinal confinement frequency $ \omega_\parallel $ along the axis of the cavity (x axis). Therefore, we can describe the dynamics within an effective one-dimensional model by quantizing the atomic motional degree of freedom along the $ x $ axis only.

In the dispersive regime of  atom-field interaction where the laser pump is far-detuned from the atomic resonance ($ \Delta_a=\omega_a - \omega_L \gg \Gamma_a $ where $ \Gamma_a$ is the atomic linewidth), the excited electronic state of the atoms can be adiabatically eliminated and spontaneous emission can be neglected \cite{Ritsch}. The many-body Hamiltonian of the BEC can be written as
\begin{eqnarray} \label{H1_BEC}
&& \hat  H_{BEC}=\int_{-L/2}^{L/2}dx \hat \psi^\dag(x) \hat H_0 \hat \psi(x) +\hat H_s ,
\end{eqnarray}
in which
\begin{subequations} \label{H_0&s}
   \begin{eqnarray} \label{H_0}
     && \hat H_0= \frac{-\hbar^2}{2m_a} \frac{d^2}{dx^2}+ \hbar U_0 \cos^2(k_0 x) \hat a^\dag \hat a + V_{ext}^{\lVert}(x), \\
     && \hat H_s= \frac{1}{2} U_s  \int_{-L/2}^{L/2} dx \hat \psi^{\dag}(x)  \hat \psi^{\dag}(x) \hat \psi(x)  \hat \psi(x)  ,
   \end{eqnarray}
\end{subequations}
where $ \hat \psi(x) $ is the annihilation operator of the atomic field, $ U_0=-g_a^2/\Delta_a $ is the optical lattice barrier height per photon which represents the atomic backaction on the field in the dispersive regime, $ g_a $ is the vacuum Rabi frequency or atom-field coupling constant, $ U_s=4\pi \hbar^2 a_s/m_a $, and $ a_s $ is the two-body \textit{s}-wave scattering length	 \cite{Ritsch,Domokos}.

In Eq. \ref{H_0&s}(a), the longitudinal trapping potential $ V_{ext}^{\lVert}(x)= m_a \omega_{\lVert}^2 x^2/2 $ can be approximately ignored. In an effective one-dimensional model this approximation is valid as long as $ \omega_\bot \gg \omega_\lVert $ so that the periodic potential of the optical lattice in the longitudinal direction is only slightly modified by $ V_{ext}^{\lVert}(x) $. Additionally, the energy arising from the atom-atom interaction has to be smaller than the energy splitting of the transverse vibrational states $ \hbar \omega_\bot $ which implies that the linear density of the condensate is smaller than $ 1/2a_s $ \cite{Morsch,Cigar}.

In the weakly interacting regime, i.e., $ U_0 \langle \hat a^\dag \hat a  \rangle \le 10\omega_R $ where $ \omega_R=\hbar k_0^2/2m_a $ is the recoil frequency of the condensate atoms, one can restrict the atomic field operator $\hat \psi(x) $ to the first two symmetric momentum side modes with momenta $ \pm 2\hbar k_0 $ which are excited by the atom-light interaction \cite{Domokos2}.  In this manner, because of the parity conservation and considering the Bogoliubov approximation \cite{Nagy}, the atomic field operator can be expanded as the following single-mode quantum field:
\begin{eqnarray} \label{si1}
&& \hat \psi(x)= \sqrt{N/L}+ \phi_2(x) \hat d ,
\end{eqnarray}
where $ \phi_2(x)= \sqrt{2/L}\cos(2k_0x) $ and the Bogoliubov mode $ \hat d $ corresponds to the quantum fluctuations of the atomic field around the classical condensate mode $ \sqrt{N/L} $. In this expansion we have not only neglected terms proportional to $ \cos(2mk_0x) $ with $ m \ge 2 $ but also the terms with nonzero quasimomenta \cite{dalafi1}.
Based on the numerical results obtained from \cite{Cigar} even the transition probability to the state with $ m=2 $ is very low. As has been shown in Refs. \cite{MeystreBEC, dalafi qpt}, the scattering to these extra modes due to the atom-atom interaction, or interaction with  $ V_{ext}^{\lVert}(x) $, can be simulated as a damping process and may be incorporated into the noise that affects the matter field.

In the case that the system does not have parity symmetry, for example, when the BEC is trapped inside a ring cavity, one should also consider $ \rm sine $ modes which in our model have been set aside \cite{MeystreBEC2,MeystreBEC3}. By substituting the atomic field operator, Eq. (\ref{si1}), into the Hamiltonian of Eq. (\ref{H1_BEC}), we arrive at the following form for the Hamiltonian of the atomic BEC subsystem
	\begin{eqnarray}
	&&  \hat H_{BEC}\! = \! \!  \hbar\delta_0 \hat a^\dag \hat a \!+\!  \hbar \omega_d \hat d^\dag \hat d \!+ \! \hbar G_0\hat a^\dag \hat a (\hat d  + \hat d^\dag) \! +  \! \hat H_{sw} \!\! + \hat H_{CK} , \label{H_BEC} \\
	&& \hat H_{sw}= \hbar\frac{\omega_{sw}}{4} (\hat d^2 + \hat d^{\dag 2}) , \label{H_sw} \\
	&& \hat H_{CK}=  \hbar \eta \hat a^\dag \hat a \hat d^\dag \hat d  , \label{H_ck}
	\end{eqnarray}
where $ \delta_0=NU_0/2 $, $ \omega_d=4\omega_R + \omega_{sw} $ is the effective frequency of the Bogoliubov mode in the atomic BEC, $ G_0=\sqrt{2N}U_0/4 $ is the strength of an optomechanical-like coupling between the Bogoliubov mode of the BEC and the intracavity field, $ \omega_{sw}= 8\pi\hbar N a_s/(m_a L w^2) $ is the \textit{s}-wave scattering frequency of atom-atom interaction ( with $ w $ being the waist radius of the optical mode), and  $ \eta=U_0/2 $ is the cross-Kerr (CK) coefficient.

The first term in Eq. (\ref{H_BEC}) leads to a shift of the cavity detuning in Eq. \ref{H_c,m,opt}(a), i.e., $ \Delta_c \to \Delta_0=\Delta_c + NU_0/2 $ which can be interpreted as an effective Stark-shifted detuning. The second term describes the energy of the Bogoliubov mode $ \hat d $. The third term is an optomechanical-like interaction which corresponds to the linear radiation pressure coupling of the Bogoliubov mode and the optical field. In this manner, the Bogoliubov mode plays the role of another MO. The fourth term is the atom-atom interaction energy  which plays the role of the \textit{atomic parametric amplifier} and is responsible for the generation of atomic squeezed state. The last term denotes the CK nonlinear coupling between the intracavity field and the Bogoliubov mode. As has been shown in Ref. \cite{dalafi4}, in the case of $ \eta/ G_0\ll 1 $ the effect of this term is negligible. Therefore, we will ignore the CK term in our calculations.

\subsection{Modulation of the atomic collisions}
Here, we consider a time modulation of the atomic collisions at twice of the Bogoliubov mode of the BEC, i.e., we assume $ \omega_{sw}(t)= \omega_{sw}\big(1+\varepsilon \cos (2\omega_d t+\varphi_d)\big ) $ where $ \varepsilon $ and $ \varphi_d $ denote, respectively, the amplitude and the phase of modulation. It can be realized by the time modulation of the scattering length $ a_s $ via the modulation of the electromagnetic trap, or the modulation of the density of the BEC by changing the trap stiffness via the intensity modulation of the pump laser, thereby modulating the speed of sound \cite{Jaskula}.
Applying the RWA on the Hamiltonian (\ref{H_sw}) one can find
\begin{eqnarray} \label{H_sw_mod}
&& \hat H_{sw}(t) \approx \frac{i \hbar}{2} (\lambda_d \hat d^{\dag 2}  e^{-2i\omega_d t}- \lambda_d^\ast \hat d^2 e^{2i\omega_d t}),
\end{eqnarray}
where $ \lambda_{d}=-i\varepsilon \omega_{sw} e^{-i\varphi_d}/4 $ can be taken real by fixing the phase $ \varphi_d $ . As can be seen, the Hamiltonian (\ref{H_sw_mod}) describes a Bogoliubov phonon analog of the DPA where the quantum fluctuation of the Bogoliubov mode plays the role of the signal mode in the DPA. It means that the coherent modulation of the frequency of the atomic collisions leads to the amplification of quantum vacuum fluctuations of the Bogoliubov mode, i.e., the dynamical Casimir emission of Bogoliubov phonons (Bogoliubov-type Casimir phonons).

\section{system dynamics}\label{sec3}
Based on the above considerations, one can rewrite the total Hamiltonian of the system in the frame rotating at the driving laser frequency ($ \omega_L $) as follows:
\begin{eqnarray}
&& \mathcal{\hat H}_{tot}=\hbar \Delta_0 \hat a^\dag \hat a + \hbar \omega_m \hat b^\dag \hat b + \hbar \omega_d \hat d^\dag \hat d + i \hbar E_L(\hat a^\dag - \hat a ) \nonumber \\
&& \qquad \qquad \qquad -\hbar g_0 \hat a^\dag \hat a (\hat b+\hat b^\dag) + \hbar G_{0} \hat a^\dag \hat a (\hat d +\hat d^\dag)  \nonumber \\
&& \qquad \qquad \qquad + i \frac{\hbar }{2} (\lambda_m\hat b^{\dag2} e^{-2i\omega_m t}+ \lambda_m^\ast \hat b^2 e^{2i\omega_m t}) \nonumber \\
&& \qquad \qquad \qquad + i  \frac{ \hbar}{2} (\lambda_d \hat d^{\dag 2}  e^{-2i\omega_d t}- \lambda_d^\ast \hat d^2 e^{2i\omega_d t}) .
\end{eqnarray}
The corresponding QLEs can be written as
\begin{subequations} \label{Langevin1}
\begin{eqnarray}
&&\!\!\!\!\!\!\!\!\!\!\!\!\!\! \dot {\hat a} \! =\!\! -(i \Delta_0 \!+\! \frac{\kappa}{2}) \hat a\! + \! i g_0 (\hat b \!+\! \hat b^\dag) \hat a\!  - \! i G_0 (\hat d \! + \!\hat d^\dag) \hat a \!+\! E_L \!\!+ \!  \! \sqrt{\kappa} \hat a_{in} , \\
&&\!\!\!\!\!\!\!\!\!\!\!\!\!\!   \dot {\hat b} \! =\! -(i\omega_m +\frac{\gamma_m}{2}) \hat b +ig_0 \hat a^\dag \hat a \!+\! \lambda_m e^{-2i\omega_m t} \hat b^\dag \! + \! \sqrt{\gamma_m} \hat b_{in}, \\
&&\!\!\!\!\!\!\!\!\!\!\!\!\!\!   \dot {\hat d} = -(i \omega_d + \dfrac{\gamma_d}{2}) \hat d -i G_0 \hat a^\dag \hat a + \lambda_d e^{-2i\omega_d t} \hat d^\dag \! + \!\sqrt{\gamma_d} \hat d_{in}.
\end{eqnarray}
\end{subequations}

Here, the cavity-field quantum vacuum fluctuation $\hat a_{in}(t)$ satisfies the Markovian correlation functions, i.e., $\langle\hat a_{in}(t)\hat a_{in}^{\dagger}(t^{\prime})\rangle=(\bar n_{ph}+1)\delta(t-t^{\prime})$ and $ \langle\hat a_{in}^{\dagger}(t)\hat a_{in}(t^{\prime})\rangle=\bar n_{ph}\delta(t-t^{\prime}) $ with the average thermal photon number $\bar n_{ph}$ which is nearly zero at optical frequencies \cite{Gardiner}. We also assume that the Brownian noises  $ \hat b_{in} $ and $ \hat d_{in} $ affecting, respectively, the mechanical mode and the Bogoliubov mode of the BEC (regarded as a formal analog of an MO) have Markovian behavior which is valid for oscillators with high quality factors \cite{MeystreBEC, vitali noise membrane}. Their correlation functions can be written as $ \langle\hat b_{in}(t)\hat b_{in}^{\dagger}(t^{\prime})\rangle=(\bar n_{m}+1)\delta(t-t^{\prime}) $, $ \langle\hat b_{in}^{\dagger}(t)\hat b_{in}(t^{\prime})\rangle=\bar n_{m}\delta(t-t^{\prime}) $,
 $ \langle\hat d_{in}(t)\hat d_{in}^{\dagger}(t^{\prime})\rangle=(\bar n_{d}+1)\delta(t-t^{\prime}) $, and $ \langle\hat d_{in}^{\dagger}(t)\hat d_{in}(t^{\prime})\rangle=\bar n_{m}\delta(t-t^{\prime}) $  where $ \bar n_m=[\exp(\hbar \omega_m/k_B T)-1]^{-1} $  and $ \bar n_d=[\exp(\hbar \omega_d/k_B T)-1]^{-1} $ are the thermal excitations of the mechanical and Bogoliubov modes, respectively. It should be noted that the noise sources are assumed to be uncorrelated for the different modes of both the matter and light fields.

The QLEs (\ref{Langevin1}a)-(\ref{Langevin1}c) can be solved analytically by adopting a linearization procedure in which the operators are expressed as the sum of their classical mean values and small fluctuations, i.e., $ \hat o = \bar o + \delta \hat o $ with $ \langle \delta \hat o^\dag \delta \hat o \rangle / \langle \hat o^\dag \hat o \rangle \ll 1  $ ($ o=a,b,d $).
The linearized QLEs describing the dynamics of the quantum fluctuations are given by
\begin{subequations} \label{Langevin-linearized}
	\begin{eqnarray}
	&&\! \! \!\! \! \!\!\!\!\!\!\! \delta \dot { \hat a}\! =\! -(i \bar \Delta_0 \!+\! \frac{\kappa}{2}) \delta \hat a \!+\! i g (\delta \hat b \! + \! \delta  \hat b^\dag) \! - \! i G (\delta \hat d \! +\! \delta \hat d^\dag) \! + \! \sqrt{\kappa} \hat a_{in} , \\
	&&\! \! \!\! \! \!\!\!\!\!\!\! \delta \dot {\hat b} \! =\! -(i\omega_m \!\! +\! \! \frac{\gamma_m}{2}) \delta \hat b \! + \!ig (\! \delta \hat a^\dag \! + \! \delta \hat a ) \!+\! \lambda_m e^{-2i\omega_m t} \! \delta \hat b^\dag \! \!+ \! \!\! \sqrt{\gamma_m} \hat b_{in}, \\
	&&\! \! \!\! \! \!\!\!\!\!\!\! \delta \dot {\hat d} \! =\! -(i \omega_d \! + \! \dfrac{\gamma_d}{2}) \delta \hat d  \! -i G(\delta \hat a^\dag \!\! + \! \delta \hat a ) \! +\!\! \lambda_d e^{-2i\omega_d t} \! \delta \hat d^\dag \! \! +\!\! \sqrt{\gamma_d} \hat d_{in},
    \end{eqnarray}
\end{subequations}
where $ g=g_0 \bar a $ and $ G = G_0 \bar a $ are the enhanced-optomechanical coupling strengths of the moving mirror and the Bogoliubov mode of the BEC to the intracavity field, respectively, and $ \bar \Delta_0 = \Delta_0 -2g_0 {\rm{Re}}  (\bar b) +2 G_{0} {\rm{Re}}(\bar d ) \approx \Delta_0 $.

From the linearized QLEs (\ref{Langevin-linearized}a)-(\ref{Langevin-linearized}c), one can deduce the following linearized Hamiltonian in the Schr\"{o}dinger picture
\begin{eqnarray} \label{H-Linear}
&&  \mathcal{\hat H}_L= \hbar \bar \Delta_0 \delta \hat a^\dag \delta \hat a + \hbar \omega_m \delta \hat b^\dag \delta \hat b + \hbar \omega_d \delta \hat d^\dag \delta \hat d \nonumber \\
&& \qquad  - \hbar g (\delta \hat a + \delta \hat a^\dag) (\delta \hat b + \delta \hat b^\dag)+\hbar G (\delta \hat a + \delta \hat a^\dag) (\delta \hat d + \delta \hat d^\dag) \nonumber \\
&& \qquad + i\frac{\hbar }{2}(\lambda_m \delta \hat b^{\dag 2} e^{-2i\omega_m t} - \lambda_m^\ast \delta \hat b^2 e^{2i\omega_m t}) \nonumber \\
&& \qquad + i\frac{\hbar }{2}(\lambda_d \delta \hat d^{\dag 2} e^{-2i\omega_d t} - \lambda_d^\ast \delta \hat d^2 e^{2i\omega_d t}),
\end{eqnarray}
or in the interaction picture
\begin{eqnarray} \label{H-Linear-interaction}
&&  \mathcal{\hat H}_L^{(I)}= - \hbar g (\delta \hat a e^{-i\bar \Delta_0 t} + \delta \hat a^\dag e^{i\bar \Delta_0 t}) (\delta \hat b e^{-i\omega_m t}+ \delta \hat b^\dag e^{i\omega_m t}) \nonumber  \\
&& \qquad \quad +\hbar G (\delta \hat a e^{-i\bar \Delta_0 t}  + \delta \hat a^\dag e^{i\bar \Delta_0 t} ) (\delta \hat d  e^{-i\omega_d t} + \delta \hat d^\dag e^{i\omega_d t}) \nonumber \\
&& \qquad \quad + i\frac{\hbar }{2}(\lambda_m \delta \hat b^{\dag 2} - \lambda_m^\ast \delta \hat b^2 ) + i\frac{\hbar }{2}(\lambda_d \delta \hat d^{\dag 2} - \lambda_d^\ast \delta \hat d^2).
\end{eqnarray}

To proceed further, we assume that the frequency of the Bogoliubov mode of the BEC, $ \omega_d $, can be matched to the mechanical frequency ($ \omega_d \approx \omega_m $) via the atomic collisions frequency $ \omega_{sw} $ or through the recoil frequency $ \omega_R $ via the driving laser frequency. Therefore, we restrict ourselves to the red-detuned regime of cavity optomechanics where $ \Delta_0 \approx \omega_m \approx \omega_d $. In this regime and within the RWA where the BEC-cavity mode as well as the MO-cavity mode couplings are analogous to the beam-splitter interaction, Eqs. (\ref{Langevin-linearized}a)-(\ref{Langevin-linearized}c) can be rewritten as follows
\begin{subequations} \label{Langevin-BS}
	\begin{eqnarray}
	&& \delta \dot { \hat a} = -\frac{\kappa}{2} \delta \hat a + i g  \delta \hat b - i G \delta \hat d + \sqrt{\kappa} \hat a_{in} , \\
	&& \delta \dot {\hat b}  = -\frac{\gamma_m}{2} \delta \hat b + i g \delta \hat a + \lambda_m \delta \hat b^\dag +  \sqrt{\gamma_m} \hat b_{in}, \\
	&& \delta \dot {\hat d}  = - \dfrac{\gamma_d}{2} \delta \hat d  -i G  \delta \hat a + \lambda_d \delta \hat d^\dag  +  \sqrt{\gamma_d} \hat d_{in}.
	\end{eqnarray}
\end{subequations}
Now, by defining the quadratures $ \delta \hat X_o=(\hat o+\hat o^{\dagger})/\sqrt{2} $ and $ \delta \hat P_o=(\hat o-\hat o^{\dagger})/\sqrt{2}i $ ($ o=a,b,d $) we can express the linearized Eqs. (\ref{Langevin-BS}a)-(\ref{Langevin-BS}c) in the compact matrix form as
\begin{eqnarray} \label{udot}
&&\delta \dot {\hat u}(t)= A ~\delta \hat u(t) + \hat N(t),
\end{eqnarray}
where the vector of continuous-variable fluctuation operators and the corresponding vector of noises are given by $ \hat u=(\delta \hat X_a,\delta \hat P_a,\delta \hat X_b, \delta \hat P_b,\delta \hat X_d,\delta \hat P_d)^T $ and $ \hat N=(\sqrt{\kappa}\hat X_a^{in},\sqrt{\kappa}\hat P_a^{in},\sqrt{\gamma_m}\hat X_b^{in},\sqrt{\gamma_m}\hat P_b^{in}, \sqrt{\gamma_d} \hat X_d^{in},\sqrt{\gamma_d} \hat P_d^{in} )^T $, respectively. Here, $ \hat X_o^{in}=(\hat o_{in}+\hat o_{in}^{\dagger})/\sqrt{2} $ and $ \hat P_o^{in}=(\hat o_{in}-\hat o_{in}^{\dagger})/\sqrt{2}i $ ($ o=a,b,d $).
Furthermore, the time-independent drift matrix $ A $ is given by
\begin{eqnarray} \label{A}
&&\!\!\!\!\!\!\!\!\!\!\!\!  A\!=\! \left( \begin{matrix}
{-\frac{\kappa}{2}} & {0} & {0} & {-g} & {0} & {G}  \\
{0} & {-\frac{\kappa}{2}} & {g} & {0} & {-G} & {0}  \\
{0} & {-g} & {\!\lambda_m\!-\!\frac{\gamma_m}{2}} & {0} & {0} & {0}  \\
{g} & {0} & {0} & {-(\lambda_m\!+\!\frac{\gamma_m}{2})} & {0} & {0}  \\
{0} & {G} & {0} & {0} & {\lambda_d -\frac{\gamma_d}{2}} & {0}  \\
{-G} & {0} & {0} & {0} & {0} & {-(\lambda_d\!+\!\frac{\gamma_d}{2} )}  \\
\end{matrix} \right).
\end{eqnarray}
In the steady state ($ \kappa t \gg 1 $) with the condition $ \kappa \gg \gamma_{m,d} $, the RWA leads to the good-cavity limit, i.e., $ \omega_m \gg \kappa $. The formal solution of Eq. (\ref{udot}) can be obtained by integration. On the other hand, the symmetric covariance matrix with entries given by $ V_{ij}=\langle \hat u_i(t) \hat u_j(t) +\hat u_j(t) \hat u_i(t) \rangle /2$ fully characterizes the quantum correlations of the system quadratures whose dynamics can be expressed as the following equation
\begin{eqnarray} \label{Vdot}
&& \frac{d V}{dt}=  A ~ V + V ~ A^T + D ,
\end{eqnarray}
where $ D $ is the diffusion matrix defined as
\begin{eqnarray} \label{D}
&& D_{ij} \delta (t-t')=\frac{1}{2} \langle \hat N_i(t) \hat N_j(t')+ N_j(t') N_i(t) \rangle .
\end{eqnarray}
 In the steady state the covariance matrix $ V $ solves the Lyapunov equation
  \begin{eqnarray} \label{V}
  &&   A ~ V + V ~ A^T = - D,
  \end{eqnarray}
with
\begin{eqnarray}
&& \! \!\!\!\!\!\!\!\!\!\!\!\!\!\! D \!= \! {\rm {Diag}} \Big [\frac{\kappa}{2},\frac{\kappa}{2},\frac{\gamma_m}{2}n^{\prime}_m,\frac{\gamma_m}{2}n^{\prime}_{m},\frac{\gamma_d}{2}n^{\prime}_d, \frac{\gamma_d}{2}n^{\prime}_d\Big], \!\!
\label{D_ij_standard}
\end{eqnarray}
where $ n^{\prime}_m=2\bar n_m+ 1 $ and  $ n^{\prime}_d=2\bar n_d +1 $.

\section{QLE{\scriptsize s} in Fourier space}\label{sec4}
The set of differential equations (\ref{Langevin-BS}) can be solved in the frequency space by the Fourier transformation, $ \hat O(t)= (1/\sqrt{2\pi}) \int_{-\infty}^{\infty} d\omega \hat O(\omega) e^{-i\omega t} $. The solution can be written in the following form

\begin{subequations}
\begin{eqnarray}
&& \!\! -i\omega \delta \hat a(\omega)  =\! -[\kappa/2 \! +\! i\Sigma_a(\omega)] \delta \hat a(\omega) \! + \!  \tilde \lambda_a(\omega) \delta \hat a^\dagger(\omega) \! + \!\!\! \sqrt{\kappa} \hat A_{in}(\omega) , \label{a_omega} \nonumber  \\
&& \\
&&\!\! -i\omega \delta \hat b(\omega)=\! -[\gamma_m/2 \!- \! i\Sigma_b(\omega)] \delta \hat b(\omega) \! + \! \tilde \lambda_b(\omega) \delta \hat b^\dagger(\omega) \! + \!\!\! \sqrt{\gamma_m} \hat B_{in}(\omega), \label{b_omega} \nonumber  \\
&& \\
&& \!\! -i\omega \delta \hat d(\omega)= \! -[\gamma_d/2 \! + \! i \Sigma_d(\omega)] \delta \hat d(\omega) \! + \! \tilde \lambda_d(\omega) \hat d^\dagger(\omega)\! + \!\!\! \sqrt{\gamma_d} \hat D_{in}(\omega). \label{d_omega}  \nonumber \\
\end{eqnarray}
\end{subequations}
Here, the self-energies are given by
\begin{subequations}
	\begin{eqnarray}
	&& i \Sigma_a(\omega)= g^2 \frac{\gamma_m/2-i \omega}{(\gamma_m/2-i \omega)^2-\vert \lambda_m \vert^2} + G^2 \frac{\gamma_d/2-i \omega}{(\gamma_d/2-i \omega)^2-\vert \lambda_d \vert^2} , \nonumber \\
	&& \\
	&& i\Sigma_b(\omega)= g^2 \frac{\kappa/2 -i(\omega-\Sigma_s(\omega))}{[\kappa/2-i(\omega-\Sigma_s(\omega))]^2- \bar \Lambda_s^2(\omega)} , \label{S_b} \\
	&&  i\Sigma_d(\omega)= G^2 \frac{\kappa/2 - i(\omega-\Sigma_m(\omega)) }{[\kappa/2 - i(\omega-\Sigma_m(\omega))]^2 - \Lambda_m^2(\omega)} ,
	\end{eqnarray}
\end{subequations}
with
\begin{subequations}
\begin{eqnarray}
&& i \Sigma_s(\omega)=G^2\frac{\gamma_d/2- i\omega}{(\gamma_d/2-i\omega)^2 - \vert \lambda_d \vert^2} ~, \label{sigma_s}  \\
&& i\Sigma_m(\omega)= g^2 \frac{\gamma_m/2-i\omega}{(\gamma_m/2-i\omega)^2 - \vert \lambda_m \vert^2} ~ , \label{sigma_m} \\
&& \bar \Lambda_s(\omega)=\lambda_d G^2 \frac{1}{(\gamma_d/2-i\omega)^2 - \vert \lambda_d \vert^2} ~, \label{lambda_s} \\
&& \Lambda_m(\omega)=\lambda_m  g^2 \frac{1}{(\gamma_m/2-i\omega)^2 - \vert \lambda_m \vert^2} \label{lambda_m} ~.
\end{eqnarray}
\end{subequations}
The \textit{induced} frequency-dependent parametric amplification factors which are analogous to the gain factors in the conventional DPA are given by
\begin{subequations}
	\begin{eqnarray}
     &&\!\!\!\!\!\!\!\!\! \tilde \lambda_a(\omega)=\frac{ g^2  \lambda_m}{(\gamma_m/2-i \omega)^2-\vert \lambda_m \vert^2} + \frac{G^2 \lambda_d}{(\gamma_d/2-i \omega)^2-\vert \lambda_d \vert^2} , \label{lambda_a_omega} \\
     &&\!\!\!\!\!\!\!\!\! \tilde \lambda_b(\omega)= \lambda_m + g^2 \frac{\bar \Lambda_s(\omega)}{[\kappa/2-i(\omega-\Sigma_s(\omega))]^2- \bar \Lambda_s^2(\omega)} ~, \label{lambda_b_omega} \\
     &&\!\!\!\!\!\!\!\!\! \tilde \lambda_d(\omega)= \lambda_{d} + G^2 \frac{\Lambda_m(\omega)}{[\kappa/2 - i(\omega-\Sigma_m(\omega))]^2 - \Lambda_m^2(\omega)} ~,  \label{lambda_d_omega}
	\end{eqnarray}
\end{subequations}
and are responsible for the generation of the Casimir photons or phonons.
Moreover, the generalized noise operators are given by
\begin{subequations}
\begin{eqnarray}
&& \hat A_{in}= \hat a_{in} + ig \sqrt{\frac{\gamma_m}{\kappa}} \frac{\gamma_m/2-i \omega}{(\gamma_m/2-i \omega)^2-\vert \lambda_m \vert^2} \left[ \hat b_{in} + \frac{\lambda_m}{\gamma_m/2-i\omega} \hat b^\dagger_{in}  \right] \nonumber \\
&& \qquad -iG \sqrt{\frac{\gamma_d}{\kappa}} \frac{\gamma_d/2-i \omega}{(\gamma_d/2-i \omega)^2-\vert \lambda_d \vert^2} \left[ \hat d_{in} + \frac{\lambda_s}{\gamma_d/2-i\omega} \hat d^\dagger_{in}  \right] , \\
&& \hat B_{in}(\omega)= \hat b_{in}(\omega) +\frac{1}{g} \sqrt{\frac{\kappa}{\gamma_m}} \left[ i\bar \Lambda_b(\omega) \hat a_{in}^\dag (\omega) - \Sigma_b(\omega) \hat a_{in}(\omega) \right] \nonumber  \\
&&\quad -\frac{i}{gG} \sqrt{\frac{\gamma_d}{\gamma_m}} \Sigma_s(\omega) \left[ \left(\frac{\lambda_d}{\gamma_d/2 - i\omega} \bar \Lambda_b(\omega) - i\Sigma_b(\omega) \right) \hat d_{in}(\omega)  \right. \nonumber \\
&&\qquad\quad\qquad\quad  \left.  \left( \bar \Lambda_b(\omega)- i\Sigma_b(\omega) \frac{\lambda_d}{\gamma_d/2 - i\omega}  \right) \hat d_{in}^\dag(\omega) \right], \\
&& \hat D_{in}(\omega)= \hat d_{in}(\omega) + \sqrt{\frac{\kappa}{\gamma_d}}  \left[ \frac{\Sigma_d(\omega)}{G} \hat a_{in}(\omega) - i G \bar \Lambda_d(\omega) \hat a_{in}^\dag(\omega) \right] \nonumber \\
&& \quad -\frac{\Sigma_m(\omega)}{g}(\omega)  \sqrt{\frac{\gamma_m}{\gamma_d}} \left[ \frac{\Sigma_d(\omega)}{G} \hat b_{in}(\omega) + i G \bar \Lambda_d(\omega)  \hat b_{in}^\dagger(\omega)   \right],
\end{eqnarray}
\end{subequations}
where  $  \bar \Lambda_b(\omega)= (\tilde \lambda_b(\omega)-\lambda_m) /g^2 $ and $ \bar \Lambda_d(\omega)=(\tilde \lambda_d(\omega)-\lambda_d) /G^2 $.

 As is evident, by turning on the modulation (i.e., $\lambda_{m,d} \neq 0$), the mechanics and the atomic collisions do indeed mediate a parametric-amplifier-like effective squeezing interaction for the cavity mode which is also frequency-dependent (see Eq. (\ref{lambda_a_omega})), unlike the case of a conventional DPA. More importantly, the time  modulation of the atomic collisions and parametric driving of the MO simultaneously amplify the vacuum fluctuations of the cavity field resulting in the generation of the Casimir photons in the \textit{coheren}t regime, which will be detailed in Sec. \ref{sec5}. Furthermore, as we will show, the time modulation of the atomic collisions (mechanical mode) amplifies indirectly the mechanical (atomic) vacuum fluctuations through the second term in Eq. (\ref{lambda_b_omega}) (Eq. (\ref{lambda_d_omega})) which leads to the dynamical Casimir emission of the mechanical (Bogoliubov) phonons.

Let us now find the effective damping rates of the phononic modes of the moving mirror and the BEC. We are interested in the on-resonance case, $ \omega= 0$, where the shifted mechanical frequency is zero and $ \Gamma_{op}^{m(d)}=-2{\rm Im} \Sigma_{b(d)}(\omega) $ is maximum. In the on-resonance case the effective mechanical (atomic) damping rate $ \Gamma_{m(d)} $ can be given by
\begin{eqnarray} \label{gamma_eff}
&& \Gamma_{m(d)}= \gamma_{m(d)}+\Gamma_{op}^{m(d)}=\gamma_{m(d)} [1+\mathcal{C}_{m(d)}] ~ ,
\end{eqnarray}
where $ \mathcal{C}_m $($ \mathcal{C}_d $) is the collective optomechanical cooperativity associated with the moving mirror (Bogoliubov mode),
\begin{eqnarray}
&&  \mathcal{C}_{m(d)}=  \mathcal{C}_{0(1)} \frac{1+ \mathcal{C}_{1(0)} - \xi_{d(m)}^2}{(1+ \mathcal{C}_{1(0)}-\xi_{d(m)}^2)^2- \xi_{d(m)}^2  \mathcal{C}_{1(0)}^2} ~,
\end{eqnarray}
where $\mathcal{C}_0=4g^2/\kappa \gamma_m$ and $\mathcal{C}_1= 4G^2/\kappa \gamma_d $ are the optomechanical and opto-atomic cooperativities, respectively, and $ \xi_{d(m)}=2\lambda_{d(m)}/\gamma_{d(m)}$.
Evidently, if $ \xi_{d(m)} \to 0 $ then $ \mathcal{C}_{m(d)} \to \mathcal{C}_{0(1)}/(1+\mathcal{C}_{1(0)})$. Both collective cooperativities $ \mathcal{C}_{m} $ and $ \mathcal{C}_{d} $ can be controlled by the time modulations of the MO and/or the BEC as well as through the individual cooperativities $ \mathcal{C}_{0} $ and $ \mathcal{C}_{1} $.

Based on  the Routh-Hurwitz criterion \cite{Routh} for the optomechanical stability condition, the parameters $ \lambda_{m} $ and $ \lambda_{d} $ should satisfy the condition $ \lambda_{m(d)} \le \lambda_{m(d)}^{max}=\Gamma_{m(d)}/2= \gamma_{m(d)}/2 (1+ \mathcal{C}_{m(d)})$. The interesting case is the regime with $ \mathcal{C}_{m(d)} > 1 $ where the amplification of generated Casimir photons and phonons can occur if
\begin{eqnarray} \label{phononic coherent regime}
&& \frac{ \gamma_{m(d)}}{2} < \lambda_{m(d)} < \frac{ \gamma_{m(d)}}{2} [1+ \mathcal{C}_{m(d)}] .
\end{eqnarray}

Analogous to the phononic damping rates, the optomechanically-induced cavity damping rate is defined as $ \kappa_{op}=-2 {\rm{Im}} \Sigma_a(\omega) $. In the on-resonance case ($ \omega=0 $), $ \kappa_{op}$ is given by
\begin{eqnarray} \label{kapa_opt}
&& \kappa_{opt}= g^2 \frac{\gamma_m}{\frac{\gamma_m^2}{4}-\vert \lambda_m \vert^2} + G^2 \frac{\gamma_d}{\frac{\gamma_d^2}{4}-\vert \lambda_d \vert^2} \nonumber \\
&& \qquad =\kappa \left[ \frac{\mathcal{C}_0}{1-\xi_m^2} + \frac{\mathcal{C}_1}{1-\xi_d^2} \right] := \kappa \mathcal{C}_a ~ .
\end{eqnarray}
Note that if the condition (\ref{phononic coherent regime}) is satisfied then $ \kappa_{opt} <0 $ and also $ \tilde \lambda_a[\omega]  $ increases. Consequently, if the optomechanically-induced cavity damping rate becomes negative, then the effective cavity damping rate defined by $ \kappa_{\rm eff}= \kappa + \kappa_{opt}= \kappa (1+\mathcal{C}_a) $ decreases which leads to the heating of the cavity field.

\section{GENERATION OF CASIMIR PHOTONS AND PHONONS}\label{sec5}
\begin{figure}
	\includegraphics[width=9cm]{2.pdf}
	\caption{(Color online) A schematic diagram describing different channels for the generation and amplification of the DCE of photons and mehchanical and Bogoliubov phonons. The time modulations of the BEC and the MO establish coherent channels for induced amplification of the photon vacuum fluctuations resulting in the DCE of photons. Moreover, the time modulation of the BEC (MO) not only causes the amplification of the vacuum fluctuations of the Bogoliubov phonons (MO's phonons), but also provides a coherent channel to induce a frequency-dependent parametric amplification of the vacuum fluctuations of the MO's phonons (Bogoliubov phonons).
		 }
	\label{fig2}
\end{figure}
In this section we are going to explore the possibility of generating Casimir photons and phonons in the system under consideration through the parametric amplification of the quantum vacuum in the so-called \textit{coherent} regime, within the limit of weak optomechanical coupling ($ g,G \ll \kappa $) and the red-detuned regime of cavity optomechanics.
Moreover, it should be pointed out that although there is no direct parametric amplification term for the intracavity mode in the Hamiltonian of the system [Eq.~(\ref{H-Linear})] but due to the time modulation of the atomic collisions and the mechanical spring coefficient, a frequency-dependent amplification [Eq.~(\ref{lambda_a_omega})] can be induced to the vacuum fluctuations of the cavity mode which leads to the \textit{coherent} and the \textit{dissipative} terms corresponding to the real and imaginary parts of Eq.~(\ref{lambda_a_omega}), respectively.

In order to clarify this matter let us remind how in the previous section we showed that our system resembles a DPA with an effective frequency-dependent parametric drive (in spite of an ordinary DPA whose parametric drive is frequency-independent). It should be noted that in an ordinary DPA when its parametric drive is real the interaction is called a coherent interaction.
Generally in our system, a frequency-dependent effective parametric drive like $ \tilde \lambda_a[\omega] $ satisfies the relation $(\tilde \lambda_a[\omega])^\ast=\tilde \lambda_a^\ast[-\omega] $.
 However, if $ \tilde \lambda_a[\omega] $ satisfies the relation $(\tilde \lambda_a[\omega])^\ast=\tilde \lambda_a[\omega] $ the system behaves like an ordinary DPA in a coherent regime. In this situation, $ \tilde \lambda_a[\omega] $ can be considered as an effective coherent interaction strength whose real and imaginary parts might lead to the \textit{`coherent'} and \textit{`dissipative'} behaviors. In this way, two different regimes can be distinguished depending on which part is larger than the other. In the so-called coherent regime where
\begin{eqnarray}  \label{coherent regime}
&&  \lvert \frac{{\rm Im} \tilde \lambda_a(\omega)}{{\rm Re} \tilde \lambda_a(\omega)} \vert \ll 1
\end{eqnarray}
is satistied, the \textit{coherent} term is dominant and consequently the photon generation via the DCE can be achieved. Otherwise, the \textit{dissipative} term is dominant and the photon generation via the DCE can not be amplified. The relation (\ref{coherent regime}) can be satisfied in the largely different coupling rates regime with nonzero modulation such that $ \xi_{m(d)} > 1$.

Regarding to the two phononic subsystems, i.e., the Bogoliubov and the MO modes, Eqs.~(\ref{lambda_b_omega}) and (\ref{lambda_d_omega}) show that in addition to the direct amplification of the phonon vacuum fluctuations of each subsystem due to its time modulation (the first term), there is an induced amplification (the second term) arising from the time modulation of the other subsystem indicating that there exist two channels for generation of the Casimir phonons of the BEC and the mechanical modes [see Fig.~(\ref{fig2})]. In the following, we discuss the DCE in the system under consideration for three different situations of time modulation.

\subsection{Mechanical modulation in the absence of BEC}

In Fig.~(\ref{fig3}), the steady-state mean number of generated Casimir photons and mechanical-type Casimir phonons in the absence of the BEC ($ G_0=\lambda_d=\gamma_d= 0$) have been plotted versus $ \xi_m / \xi_m^{\rm max} $ for a large value of cooperativity in the weak coupling regime. As the effective parameter $ \xi_m $ increases (due to the increase of modulation amplitude) to its maximum value $ 1+\mathcal{C}_m $ (in this case $ \mathcal{C}_m=\mathcal{C}_0 \gg 1 $) the mean numbers of the generated Casimir photons and phonons asymptotically increase. However, in order to generate considerable number of Casimir photons,  much more values of $ \xi_m $ is needed in comparison with that needed for mechanical-type Casimir phonons generation.
On the other hand, by increasing the optomechanical coupling strength between the MO and the cavity field, which is equivalent to increasing the cooperativity, more number of Casimir photons and phonons can be generated at smaller values of $ \xi_m $.
Moreover, the ratio of the damping rates, $ \kappa/\gamma_m $, can only affect the time period over which the system reaches to the steady state without any significant effect on the mean number of the generated Casimir particles at the steady state. It should be mentioned that for the parameter values given in Fig.~(\ref{fig3}), the mechanical and optical vacuum fluctuations start to be amplified for $ \xi_m / \xi_m^{\rm max} \ge 0.5 $ and 0.9, respectively.

\subsection{Modulating atomic collisions without MO modulation}
In Fig.~(\ref{fig4}) the mean number of the generated Casimir photons and mechanical/Bogoliubov-type phonons have been plotted  versus $ \xi_d / \xi_d^{\rm max} $ in the weak coupling regime ($ g,G\ll \kappa $) and in the absence of mechanical modulation ($ \xi_m=0 $). As shown in Fig.~(\ref{fig4}a), in the regime of equal optomechanical coupling strengths of the MO and the BEC with the cavity mode, $ g=G $, the steady-state mean number of the generated Casimir photons is negligibly small over the entire range of $ \xi_d / \xi_d^{\rm max} $ which means that equal couplings is corresponding to the dissipative regime for the intracavity field. However, the mean number of the generated mechanical/Bogoliubov-type Casimir phonons is considerably increased for $ \xi_d / \xi_d^{\rm max}> 0.8 $ and grows up asymptotically as $ \xi_d $ reaches to its maximum value.

\begin{figure}
	\includegraphics[width=4.29cm]{3a.pdf}
	\includegraphics[width=4.28cm]{3b.pdf}
	\caption{(Color online) (a) steady-state mean number of generated Casimir photons and (b)   mechanical-type Casimir phonons vs $ \xi_m / \xi_m^{\rm max} $ in the absence of the BEC. The red solid and black dashed lines correspond, respectively, to $ g/\kappa=0.05 $, $ \mathcal{C}_0=100 $ and $ g/\kappa=0.25 $, $ \mathcal{C}_0=2500 $. Here, we set $ \kappa/\gamma_m=10^{4} $. }
	\label{fig3}
\end{figure}

On the other hand, as shown in Fig.~(\ref{fig4}b), in the regime of largely different optomechanical coupling strengths ($ \vert g-G \vert\gg g  $) which is equivalent to the regime of largely different cooperativities, Casimir photons as well as Casimir phonons can be generated considerably by increasing the atomic collisions modulation parameter $ \xi_d $ which means that this regime corresponds to the coherent regime for the intracavity light field.
Therefore, by controlling the modulation rate of atomic collisions one can control the number of Casimir photons and phonons. Furthermore, our numerical calculations show that by increasing the difference between the optomechanical coupling rates $ g $ and $ G $ both the photonic and phononic DCEs are strengthened.  Moreover, increasing the coupling rates $ g $ and  $ G $ leads to the increase of Bogoliubov- and mechanical-type Casimir phonons, respectively.

\begin{figure}
	\includegraphics[width=4.29cm]{4a.pdf}
	\includegraphics[width=4.28cm]{4b.pdf}
	\caption{(Color online) Steady-state mean number of the generated Casimir photons and phonons vs $ \xi_d/\xi_d^{max} $ when mechanical modulation is zero ($ \xi_m=0 $) for the cases of (a) equal optomechanical coupling strengths $ g=G=0.05 \kappa $ and (b) largely different optomechanical coupling strength $ G=20g=0.1 \kappa $. The dashed black, solid red, and dotted blue lines correspond, respectively, to the Bogoliubov-type Casimir phonons, mechanical-type Casimir phonons, and Casimir photons. Here, we have set $ \gamma_m=\gamma_d=10^{-3}\kappa $.}
	\label{fig4}
\end{figure}

\begin{figure*}
	\includegraphics[width=5.85cm]{5a.pdf}
	\includegraphics[width=5.85cm]{5b.pdf}
	\includegraphics[width=5.85cm]{5c.pdf}
	\caption{(Color online) Comparison between the steady-state mean numbers of generated Casimir particles in the two regimes of equal optomechanical couplings $ g=G=0.05\kappa $ (blue dashed line) and largely different one $ G=250g=0.25\kappa $ (gray solid line) in the absence of the time modulation of the MO ($ \xi_m=0$): (a) mean number of generated mechanical-type Casimir phonons, (b) mean number of Bogoliubov-type Casimir phonons, and (c) mean number of intracavity Casimir photons vs $ \xi_d/\xi_d^{max} $. Here, we have set $ \gamma_m/\kappa=\gamma_d/\kappa=10^{-4}$.
	}
	\label{fig5}
\end{figure*}

Let us illustrate why in our system the strong amplification of vacuum fluctuations is occurred in the regime of largely different optomechanical coupling strengths (specially for photons). Recently, it has been shown \cite{JLiNJP,JLiPRA} that in the absence of parametric modulation, the dynamics of an optomechanical system with two mechanical modes is governed by the effective linearized Hamiltonian  $ \hat H_{\rm eff}/\hbar = \Delta_0 \delta \hat a^\dag \delta \hat a + \mathcal{G}(\hat B \delta \hat a^\dag + \hat B^\dag \delta \hat a) $ where $ \hat B= (g \delta \hat b - G \delta \hat d)/\mathcal{G} $ denotes a collective mode and $ \mathcal{G}=\sqrt{G^2-g^2} $ describes the rate of excitation exchange between the collective mode $ \hat B $ and the cavity field which leads to the cooling of the collective mode. The collective mode $ \hat B $ can approach its vacuum state corresponding to a two-mode squeezed state of the two mechanical modes.
In our system the Bogoliubov mode of BEC plays formally the role of a second mechanical oscillator mode and the two oscillators (MO and BEC) are driven parametrically. However, as has been shown in Ref. \cite{dalafi5} , by a suitable unitary transformation our system Hamiltonian can be transformed into an ordinary optomechanical one without any parametric modulation (similar to the above-mentioned Hamiltonian). Therefore, we can also construct a similar collective mode $\hat  B $ out of the atomic and the mechanical modes.
Note that, in general, one can consider the collective mode as a Bogoliubov-transformed mode  $ \hat B=  \delta \hat b \cosh r -  \delta \hat d \sinh r  $ with the squeezing parameter  $ r= \tanh^{-1} (g/G) $. Therefore, the ratio $ g/G $ determines how much the vacuum of the collective mode is squeezed or amplified. In particular, the vacuum of the collective mode in the limit of equal optomechanical coupling strengths ($  g/G \to 1 $) corresponds to a maximally squeezed or amplified state. However, in this limit the collective mode is decoupled from the optical mode (because $ \mathcal{G} \to 0 $), and thus the Casimir photons can no longer be amplified. That is why in our system the Casimir photons are strongly generated in the regime of largely different optomechanical coupling strengths (or equivalently, largely different cooperativities) where the collective mode $ \hat B $ interacts with the optical mode effectively.

In order to see more clearly the effects of the two regimes of equal and largely different optomechanical couplings on the steady-state mean numbers of generated Casimir photons and phonons, we have plotted the number of phonons [Fig.~(\ref{fig5}a) for mechanical-type and Fig.~(\ref{fig5}b) for Bogoliubov-type phonons] and the number of photons [Fig.~\ref{fig5}(c)] versus $ \xi_d / \xi_d^{\rm max} $ for the two mentioned regimes. As is seen in Fig. (\ref{fig5}c),  the number of generated Casimir photons in the regime of largely different couplings is always larger than that in the equal coupling strength regime which is acceptable based on the collective mode interpretation mentioned in the previous paragraph. Also, as the difference between the two couplings increases, the coherent channels or coherent regime for the intracavity light field is dominant. Consequently, we can conclude that the increases of the difference between coupling rates and of the amplitude of modulation of the atomic collision frequency are the only two important factors to amplify the generation of the Casimir photons.

On the other hand, the behavior of the generated phonons are somehow different from that of photons. As is seen from Figs.~(\ref{fig5}b) and (\ref{fig5}c), for the mechanical/Bogoliubov mode there exists a critical value of $\xi_{d}$ so that the behavior of the generated Bogoliubov or mechanical-type Casimir phonons are different below and above it. Figure (\ref{fig5}b) shows that below the critical value the number of Bogoliubov phonons in the regime of largely different optomechanical couplings is larger than that in the regime of equal couplings while the situation is reversed above the critical value. It can be interpreted using collective phononic mode in terms of $ \mathcal{G} $ which means that there is an optimum value of $ G/g $ or $ \xi_{d,m} $ to achieve the maximum number of generated phonons. However, as is seen from Fig.~(\ref{fig5}a), the behavior of the generated mechanical-type Casimir phonons is reverse in comparison with that of the Bogoliubov-type Casimir phonons. It is because of the fact that here the mechanical modulation is off ($ \xi_{m}=0 $) while the atomic modulation which drives the Bogoliubov mode is on ($ \xi_{d} \neq 0 $).

Note that in the absence of the MO modulation, the mean number of generated Casimir photons and phonons can be controlled by the effective modulation of the atomic collisions frequency ($ \xi_d $) and also the difference between the coupling rates of the cavity light field to the BEC and the MO. It should be mentioned that the same results can be obtained for the case without BEC modulation when only the MO modulation is present since the Bogoliubov mode in the BEC plays formally the role of a second MO mode.

\subsection{Simultaneous modulation of both the MO and atomic collisions}
\begin{figure*}
	\includegraphics[width=5.87cm]{6a.pdf}
	\includegraphics[width=5.95cm]{6b.pdf}
	\includegraphics[width=5.95cm]{6c.pdf}
	\caption{(Color online) steady-state mean number of generated Casimir radiations vs $ \xi_d/\xi_d^{max} $ in equal couplings regime corresponding to $ g=G=0.05 \kappa $ (red thick and blue dashed lines) and largely different couplings regime corresponding to $ G=50g=0.05 \kappa $ (black thin and green dotted lines) for two values of the mechanical parametric modulation $ \xi_m=0 $ (black thin and blue dashed lines) and $ \xi_m=0.2 $ (red thick and green dotted lines). (a) mechanical-type Casimir phonons, (b) Bogoliubov-type Casimir phonons, and (c) Casimir photons. Here, we set $ \gamma_m=\gamma_d=10^{-4}\kappa $. }
	\label{fig6}
\end{figure*}

Figure (\ref{fig6}) shows the steady-state mean number of generated Casimir phonons and photons versus $ \xi_d / \xi_d^{max} $ in the weak coupling regime and in the presence of both the BEC and MO modulations. As is expected, in the equal optomechanical couplings regime, the Casimir photons cannot be generated [Fig.~(\ref{fig6}c)] while a considerable number of the mechanical/Bogoliubov-type Casimir phonons are generated and increased by increasing $ \xi_d $ [Figs. (\ref{fig6}a) and (\ref{fig6}b)]. As is evident from Fig. (\ref{fig6}) by turning on the MO modulation the mean number of generated photons and phonons increase for each value of $ \xi_d $. A similar interpretation like that was explained in the previous subsection is valid here in the presence of both modulations of the atomic collisions frequency and the mechanical spring coefficient.

Since $ \lambda_m $ depends on the modulation amplitude of the MO  while $ \lambda_d $ depends both on the modulation amplitude of the BEC and on the atomic collisions frequency $ \omega_{sw} $, the mean number of generated Casimir photons and phonons can be controlled externally not only through the modulation parameters but also through the atomic collisions frequency which itself is experimentally controllable by the transverse trapping frequency $ \omega_{\perp} $. Also, through the input power laser and intrinsic coupling rates, one can control the regime corresponding to the generation of the Casimir particles, e.g., coherent regime for the photonic and phononic subsystems. Therefore, in contrast to other DCE proposals for photons or phonons \cite{Daviesbook.Dodonov2.Dalvit.Dodonov3.Crocce.Dodonov4.Dodonov5}, our system is more controllable. Moreover, similar to the previous subsection, the same results can be obtained by exchanging the roles of the BEC and MO modulations.

On the other hand, it has recently been shown \cite{antiDCE-work} that the coherent generation and annihilation of photons, which are respectively corresponding to the DCE and \textit{anti}-DCE in the quantum Rabi model with time-modulated atomic frequency in the dispersive, moderate coupling and weak modulation regimes \cite{Motazedifard DCE,antiDCE}, leads to the positive and negative quantum work extraction in the context of quantum \textit{thermodynamics}.  Also, it has been shown that a realistic out-of-equilibrium finite-time protocol harnessing anti-DCE allows for work extraction. The effect of the photon creation in our system can be attributed to the exchange of energy between the external modulation of the BEC/MO and the quantum vacuum fluctuations of the photonic and phononic subsystems through the coherent channels. If the energy is transferred to the quantum vacuum fluctuations, Casimir pair particles are created. Therefore, based on Ref. \cite{antiDCE-work}, one can conclude that the positive quantum work in our system can be extracted and externally controlled by the modulation parameters of the atomic collisions frequency and the mechanical spring coefficient which open a new way to the quantum thermodynamics of the DCE physics.

\section{Summary and outlooks}\label{sec6}
In summary, we have theoretically proposed and investigated a feasible experimental scheme to realize the DCE of phonons and photons in a hybrid optomechanical cavity with a moving end mirror containing an interacting cigar-shaped BEC. It is shown that by coherent modulation of the \textit{s}-wave scattering frequency of the BEC and of the mechanical spring coefficient of the moving mirror, the mechanical and atomic vacuum fluctuations are parametrically amplified which consequently lead to the generation of the mechanical- and Bogoliubov-type Casimir phonons. Also, in the regime of largely different optomechanical couplings, the quantum vacuum fluctuations of the intracavity field are indirectly amplified via the coherent channels by the MO and BEC which lead to the generation of cansiderable number of Casimir photons in comparison to the conventional DCE proposals.

One of the important advantages of the present scheme in comparison to the other proposals is its controllability. As was shown, the mean number of generated Casimir photons and phonons can be controlled externally not only through the modulation parameters but also through the atomic collisions frequency of the BEC which itself is experimentally controllable by the transverse trapping frequency.

As some interesting outlooks of the present work, one can investigate the possibility of the perfect quadrature squeezing or quadrature amplification of the MO/BEC or cavity output. Moreover, it seems that in the system under consideration due to the generation of the Casimir photons and phonons one can require the condition for simultaneously backaction noise suppression and signal amplification in order to perform single quadrature force sensing in both on- and off-resonance frequency by controlling the atomic collisions frequency. Furthermore, one can look for the condition under which the cavity spectral photon function becomes negative while the system is stable, which leads to identifying an externally controllable negative effective temperature for photons that can be responsible for the modified optomechanically induced transparency (OMIT). Finally, it seems that our proposed scheme has the potential to generate robust entanglement between the MO mode and the Bogoliubov mode of the BEC which plays formally the role of a second MO mode. We hope to report on these issues in the near future.

\textit{\textbf{Acknowledgements}}
A. M. wishes to thank the Office of Graduate Studies of the University of Isfahan and also the Iran's National Elites Foundation (INEF).
A. D. wishes to thank the Laser and Plasma Research Institute of Shahid Beheshti University for their support.

redpajama_set_name: RedPajamaArXiv


text:
Bad Characters, Male Characters, Batman: The Telltale Series Characters,
Gerry Conway/Creator
Don Newton/Creator
Male Villains
Batman Villains
New 52 Characters
Gotham City Mayors
Hamilton Hill (Batman: The Telltale Series)
Hamilton Hill
Gotham Organized Crime
Gerry Conway · Don Newton
(August 2, 2016) Batman: The Telltale Series
(August 2, 2016)
Hamilton Hill was the corrupt mayor of Gotham City.
His rise to power was due to his secret and criminal affiliation with Carmine Falcone and Thomas Wayne. Although Hill was long suspected of numerous crimes, his influence over the city ensures his immunity from the law. Upon learning that Martha Wayne planned to expose Hill's and his colleagues' corruption, Hill arranged the Waynes' deaths by hiring Joe Chill to committing the deed.
Twenty years later, Hill's grasp over Gotham was challenged by Gotham's District Attorney Harvey Dent, who posed to run for the city's next mayor. Threatened by Dent's campaign, Hill resorted to hiring the Penguin and leaked information about the Waynes' connections to Falcone in order to discredit Dent's campaign and their sponsor Bruce Wayne.
Unfortunately for Hill, the Penguin betrayed him. During a public debate between Hill and Dent, Penguin and his men, the Children of Arkham, attacked the debate and hold Hill and Dent hostage. Hill was then drugged in which the drug's influence caused him to reveal his true disdainful nature to the public. When the Batman and Catwoman attempt to save the hostages, the Penguin hold Hill at gunpoint and prepare to kill him in revenge for being involve in committing Esther Cobblepot. Hill pleaded for his life to Penguin, explaining to him that he arranged the assassinations of the Waynes all the while that was being listened by Batman. Despite Hill's pleas, Penguin brutally gunned down the mayor.
Following Hill's death, Harvey Dent automatically became the new Mayor of Gotham City.
1 Appearances of Hamilton Hill (Batman: The Telltale Series)
1 Images featuring Hamilton Hill (Batman: The Telltale Series)
1 Quotations by or about Hamilton Hill (Batman: The Telltale Series)
Character Gallery: Hamilton Hill (Batman: The Telltale Series)
Batman Villain(s)
This character, team or organization, is or was primarily an enemy of the Batman, or the Batman Family as a whole. This template will categorize articles that include it into the category "Batman Villains."
Retrieved from "https://dc.fandom.com/wiki/Hamilton_Hill_(Batman:_The_Telltale_Series)?oldid=2712331"
Batman: The Telltale Series Characters


Weaker than the first and less consistent, but also funnier and with more heart, this sequel is a contradictory gumbo. If you were a fan of the first, go see it. Otherwise, wait for streaming.
The Good: Even funnier than the first and with a lot more to say, but still carried by the undeniable charisma of Ryan Reynolds.
The first Deadpool rode a tidal wave of profanity, charm, and fourth-wall breaking to record-setting success. Underlying all of that? Nothing. That was the magic of Deadpool. It was nothing more than it appeared to be.
Enter Deadpool 2, which by the trailers, might look like more of the same. Instead, it provides a surprisingly deep story about conversion therapy, trauma, school shootings, and the justification of violence.
No, this is not a joke. While it still delivers over-the-top violence and jokes aimed at Wolverine and the DC films, these are not the core of the film.
That honor goes to the relationship between Ryan Reynolds' Deadpool and Julian Dennison's (Hunt for the Wilderpeople) Firefist. Dennison continues to prove both his comedic and dramatic chops, giving an emotional performance as a boy looking for a single friend. The two actors do a fantastic job playing off of each other, despite the often ridiculous surroundings.
While Josh Brolin delivers a surprisingly nuanced turn as cybernetic time-traveling killer Cable, it is Zazie Beetz (Atlanta) that truly steals the show as the probability-altering mercenary Domino. She has an undeniable charisma and screen presence that demands to be liked. It helps that some of the most creative scenes of the film revolve around her "I'm lucky" based powers.
The Bad: It's hard to emotionally connect with living parody.
There is a balancing act that Deadpool 2 has to accomplish, and it's not clear that it pulls it off.
Deadpool is a very likable character. He is funny, first and foremost, but how that plays out varies: he can be crass, sweet, fourth-wall breaking, physical, etc., to the same effect.
But just because he is likable, doesn't make him a character that is easy to connect to. Beyond having powers that make him essentially immortal, and thereby eliminating any tension as to "will he survive?", the sheer level of his parody makes it difficult to take anything seriously.
This all serves to make him a very enjoyable character to watch but also renders his emotional stakes meaningless. He doesn't take his own death seriously, nor the death of anyone around him, or really anything. So why should you?
Thus the balance problem. To differ from Deadpool, the sequel attempts to inject a semblance of an emotional stake, to really try to get the audience to feel for its character – but then laughs at the same attempts.
The Ugly: A romantic relationship between two women isn't played for laughs, men's sexual interest, or drama – and it's astounding.
It really is one of the strangest and most wonderful parts of Deadpool 2. Brianna Hildebrand's Negasonic Teenage Warhead returns, and this time, with Yukio (Shioli Kutsuna), her new girlfriend, by her side.
And that's it. It's just presented. Deadpool is exciting for her, and immediately has a strange bonding with Yukio that is easily one of the funniest parts of the film.
1. for the sexual intrigue of the men characters or audience 2. laughs or 3. a heavily dramatic story about their hardships.
Not so for Deadpool 2. In a now $600 million blockbuster, there is a perfectly normal to the point of mundanity romantic relationship between two teenage women.
Why is this the first significant time in the history of the genre that a queer relationship has been shown on screen, especially when Fox's X-Men franchise began as a parable for the AIDS crisis and the persecution of LGBTQ folks?
One can only hope that this isn't a unicorn. Looking at you especially, Marvel – it's time to step up your game.