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Cannes 2014: Maps To The Stars By David Cronenberg
You just do not know what to expect from David Cronenberg anymore. While his career peaked early and his heydays are clearly behind him (despite what snobs might say), he has soldiered on with his career valiantly, with a few highs (eXistenZ, A History Of Violence) and many lows (A Dangerous Method, Cosmopolis...). Worse, while I would not expect him to carry on doing the same films and going over the same themes, he seems to have lost his identity, with many of his recent output feeling rather anonymous. And now he is back on the Croisette with Maps To The Stars, a Hollywood satire.
Maps To The Stars is an ensemble films, with a mötley crüe of archetypal Hollywood monsters and oddballs: the self absorbed and ageing actress Havana Segrand (Julianne Moore), a jobbing young actor trying to make it (Robert Pattinson), a child star, Benjie Weiss (Evan Bird) who is even more rotten to the core than any grown-ups around him and his parents: "Dr" Weiss (John Cusack), a therapist/coach with some highly dubious methods, and neurotic Cristina (Olivia Williams. While Havana is trying to go back into the limelight by appearing in the remake of a film that made her mother famous (whose ghost visits her regularly), Benjie's older sister Agatha (Mia Wasikowska) arrives back to Hollywood anonymously with secrets of her own...
Maps To The Stars does not have the best of start. Most, if not all of its characters and initial situations are most probably inspired by real events (including an anecdote that was making the round about what some Johnny Depp's fans were willing to do that is too gross to even mention here). Yet as a Hollywood satire it comes across as terribly obvious, showing us a city filled with morally bankrupt monsters as seen so many times before. And the final nail on the coffin of originality being Carrie Fisher's cameo, which countless tv series and films have done previously, including Scream 3 which did earlier in better (unless this is a meta comment on Carrie Fisher's cameos in numeros films? I doubt it). Yes this is a bad, bad city with not a single redeeming feature, a sort of hell that corrupts all of hits inhabitants before spitting them out, but I would have expected a more original treatment by a man who used to conjure up such distrubing films.
Worse, the surreal scenes featuring the ghost of Havana's mothers are utterly ridiculous, looking like something straight off one of those bad sitcoms that have long given up on even trying to remain credible. Remember the Simpsons' parody of those long running TV series, in which Moe becomes an actor and whose storyline involves an affair with a resurrected mommy? We are nearly there. Unless again this is a meta comment on those? I doubt it. Finally, what with the CGI/crayon'ed flames, the least convincing in the history of cinema?
Fortunately the film improves dramatically with the presence of Mia Wasikowska. A truly Cronenbergian character both physically (her burn scars) and mentally (with her highly unstable state), she brings in a much needed touch of unease. And thankfully the script follows suit, with a nightmarish second half that gives up any pretence of realism to plunge us in the darkest core of the city of angels, with brief echoes of his previous masterpieces.
As for the cast, it's a mixed bag. Robert Pattinson here only plays a short part that could have easily been cut out. Reading a recent interview, it sounds as if he was only in there to drum up some interest for film as a mark of support for Cronenberg who offered him such a great part in Cosmopolis). Julianne Moore is lumbered with an obvious part that lacks of any real depth, even if she makes the most of it. But it is Mia Wasikowska's film, in probably her best performance to date, never chasing any sympathy and at times frankly repulsive morally, as a troubled souls damaged by the poison that is Hollywood and which has infected her whole family.
Maps To The Stars is an interesting failures, which only too briefly shows what could have been, and which is not quite the film that will bring David Cronenberg back to his previously glory.
Maps To The Stars. Canada/USA. Official Selection
Directed by David Cronenberg. Starring Mia Wasikowska, Julianne Moore, Robert Pattinson, Olivia Williams, John Cusack...
Cannes 2014: Le Meraviglie by Alice Rohrwacher
Cannes 2014: White God by Kornél Mundruczó
Cannes 2014 Results: My Two Cents
Cannes 2014: Mercuriales by Virgil Vernier
Cannes 2014 Awards: Predictions & Wishlist
Cannes 2014: Clouds Of Sils Maria by Olivier Assayas
Cannes 2014: L'homme Qu'on Aimait Trop by André Té...
Cannes 2014: Adieu Au Langage 3D by Jean-Luc Godard
Cannes 2014: Bird People by Pascale Ferran
Cannes 2014: Lost River by Ryan Gosling
Cannes 2014: Two Days, One Night by Jean-Pierre an...
Cannes 2014: A Girl At My Door by July Jung
Cannes 2014: Still The Water by Naomi Kawase
Cannes 2014 : It Follows by David Robert Mitchell
Cannes 2014: Saint Laurent By Bertrand Bonello
Cannes 2014 Day 4: Westerns, Tourists & Queues
Cannes 2014 Day 3: Saint Laurent, Les Combattants ...
Cannes 2014 Day 2: Ryan Reynolds, Mathieu Amalric ...
Cannes 2014 Day 1: Girlhood, A Hijack & Sabine Azéma
You And The Night: A Jean Rollin Electro Poem
Sundance London 2014: Talking Cats, Paul Rudd, Lo-...


Tori Hidalgo received 29 call backs, Sand Alonso received 12, and Ashley Cantu received 4. This is a great accomplishment for these young actresses. Please continue to support the arts!
My name is Samantha Mendoza, and I am a Junior at Lee High School. I love to write, but I always feel like i can do better. My favorite Subject (besides writing/newspaper) is history. I am very interested in people and how they live they're lives. That' s why newspaper is so great, I get to see/write people's stories!


text:
shop / Further Reading / Histories / The Cheese and the Worms: The Cosmos of a Sixteenth-Century Miller
The Cheese and the Worms: The Cosmos of a Sixteenth-Century Miller
(Johns Hopkins University Press, 2013) by Carlo Ginzburg
Through a study of the trial records of a 16th-century miller accused of heresy during the Inquisition, Carlo Ginzburg explores the religious and social conflicts of the time.
Buy from Amazon*
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The Great Cat Massacre: And Other Episodes in French Cultural History
In Search of Sir Thomas Browne: The Life and Afterlife of the Seventeenth Century's Most Inquiring Mind
The Spectacle of Deformity: Freak Shows and Modern British Culture
The Dark Side of Nature: Science, Society, and the Fantastic in the Work of Odilon Redon
Natural Histories: Extraordinary Rare Book Selections from the American Museum of Natural History Library
The Search for the Perfect Language
Alchemy & Mysticism
The Clockwork Universe: Isaac Newton, the Royal Society, and the Birth of the Modern World

redpajama_set_name: RedPajamaCommonCrawl


text:
Q: Java - wrapper classes and hashCode() is there any difference b/w value returned by Integer's hashCode() and intValue()? Can hashcode be negative?

A: No, there's no difference, and thus yes, it can be negative or zero.
From the Javadoc:

Returns:  a hash code value for this object, equal to the primitive int value represented by this Integer object.

A: Integer.hashCode() just returns the value, yes... although it's not a good idea to rely on that. The return value of a hash code should really just be used as an opaque value without attaching any particular meaning to it - only equality should really be taken into account. Even if Integer.hashCode() is documented to just return the value (EDIT: it is; see other answer), I'd be very wary of any code which would break if the implementation changed to return (say) value + 1.
The return value of hashCode() is certainly allowed to be negative - both here and in general.

redpajama_set_name: RedPajamaStackExchange


Gracie jiu-jitsu in St Ann, MO. Since 2011, Gracie Barra St Ann has been dedicated to utilizing our 12 founding commandments to guarantee that each and every one of our students is provided the best training. Great for kids, teenagers, women, and men, Gracie Barra focuses on defense, fitness, character development, and martial arts training for people in the St Ann area. All of our classes use Master Carlos Gracie Jr.'s program structure to cater to the need of individual who learn visually, auditorily, tactilely, or kinesthetically. If you're looking for Brazilian Jiu-Jitsu classes in St Ann or the neighboring area, schedule a visit to our school.
The Gracie Barra Academy is a fun, inviting, and dynamic environment that enables St Ann students to take on the training they need to advance through supportive and challenging Brazilian Jiu-Jitsu classes. Our atmosphere is great for anyone who respects martial arts and wants to take their health level, fitness, balance, confidence, coordination, or Jiu-Jitsu skills to the next step. Get into shape, learn how to protect yourself, dispose stress, and define your workflow by joining us today.


Whether your flight is an hour or a whole day, what you wear on a plane can make or break the ride. Here are 5 Comfy Airplane Outfits for your for your next trip.
Linen is a popular travel fabric because it's light, breathable and keeps you cool. These loose linen pants with the comfy drawstring waist are laid back and easy to wear. Team them up with a cute t-shirt, sandals and a denim jacket for a travel look that is simple and no fuss.
Stretch is important when you are on a flight which is why leggings are a natural choice for airplane outfits. Pair your favorite black leggings with a soft, long shirt or tunic and settle into your seat with a good magazine.
Many gals like the simplicity of a comfy tee for summer travel, but with air-conditioning blasting, it can get quite cold on long flights. This 3/4 length sleeve blush colored tee is the perfect solution to keep away a chill. Plus, the drawstring hem, gives it plenty of style.
A cute pair of statement sneakers adds to this modern travel look and are perfect for those long hikes through airport terminals.
If you prefer a dress when you travel, then this striped cotton shift dress is sporty and practical. Once again, 3/4 length is the favored sleeve length for summer travel. Backless sneakers with summer rope trim are easy to slip on and off at security checks.
Layering is important when you travel as temperatures change from place to place. For that reason, this cute, lightweight cotton pullover is an ideal travel piece. Wear it as is on its own, or layer it over a t-shirt or tank top. Once you arrive, roll it up and tuck into your carry-on if it's too hot outside.
6 comments on "5 Comfy Airplane Outfits for Summer Travel"
I love the outfits. My suggestion would be to wear footwear that allows you to wear socks. Most often you have to remove footwear at security, which means you will be barefoot on the floor (along with many others), if you are wearing sandals. I guess you could always carry a pair of socks to slip into if you want to go barefoot in your shoes or sandals. Just a thought!
I love to get your emails!! I loved this article as well :) .
I would like to know what you suggest to wear to a long road trip that's about 15-20 hours long?
I will travel during summer and during Thanksgiving Holidays. I live in Austin, TX and am going to Philadelphia, PA both times.
I love to travel with a long top and leggings. They are very comfortable.
Hi Ava, Linen pants are light and cool in summer but I wouldn't suggest pure linen. They're crisp and wrinkle too much, even though wrinkles are a part of the linen look. I'd suggest a linen blend that is light and comfy but less wrinkly. For example, linen/rayon blends don't wrinkle as much as linen, especially after several washings. They also have more drape.


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Faust; a Tragedy, Translated from the German of Goethe By: Johann Wolfgang von Goethe (1749-1832)
A TRAGEDY
TRANSLATED FROM THE GERMAN
WITH NOTES
CHARLES T BROOKS
SEVENTH EDITION.
BOSTON TICKNOR AND FIELDS
MDCCCLXVIII.
Entered according to Act of Congress, in the year 1856, by CHARLES T. BROOKS, In the Clerk's Office of the District Court of the District of Rhode Island.
UNIVERSITY PRESS: WELCH, BIGELOW, AND COMPANY, CAMBRIDGE.
TRANSLATOR'S PREFACE.
Perhaps some apology ought to be given to English scholars, that is, those who do not know German, (to those, at least, who do not know what sort of a thing Faust is in the original,) for offering another translation to the public, of a poem which has been already translated, not only in a literal prose form, but also, twenty or thirty times, in metre, and sometimes with great spirit, beauty, and power.
The author of the present version, then, has no knowledge that a rendering of this wonderful poem into the exact and ever changing metre of the original has, until now, been so much as attempted. To name only one defect, the very best versions which he has seen neglect to follow the exquisite artist in the evidently planned and orderly intermixing of male and female rhymes, i.e. rhymes which fall on the last syllable and those which fall on the last but one. Now, every careful student of the versification of Faust must feel and see that Goethe did not intersperse the one kind of rhyme with the other, at random, as those translators do; who, also, give the female rhyme (on which the vivacity of dialogue and description often so much depends,) in so small a proportion.
A similar criticism might be made of their liberty in neglecting Goethe's method of alternating different measures with each other.
It seems as if, in respect to metre, at least, they had asked themselves, how would Goethe have written or shaped this in English, had that been his native language, instead of seeking con amore (and con fidelità ) as they should have done, to reproduce, both in spirit and in form, the movement, so free and yet orderly, of the singularly endowed and accomplished poet whom they undertook to represent.
As to the objections which Hayward and some of his reviewers have instituted in advance against the possibility of a good and faithful metrical translation of a poem like Faust, they seem to the present translator full of paradox and sophistry. For instance, take this assertion of one of the reviewers: "The sacred and mysterious union of thought with verse, twin born and immortally wedded from the moment of their common birth, can never be understood by those who desire verse translations of good poetry." If the last part of this statement had read "by those who can be contented with prose translations of good poetry," the position would have been nearer the truth. This much we might well admit, that, if the alternative were either to have a poem like Faust in a metre different and glaringly different from the original, or to have it in simple and strong prose, then the latter alternative would be the one every tasteful and feeling scholar would prefer; but surely to every one who can read the original or wants to know how this great song sung itself (as Carlyle says) out of Goethe's soul, a mere prose rendering must be, comparatively, a corpus mortuum.
The translator most heartily dissents from Hayward's assertion that a translator of Faust "must sacrifice either metre or meaning." At least he flatters himself that he has made, in the main, (not a compromise between meaning and melody, though in certain instances he may have fallen into that, but) a combination of the meaning with the melody, which latter is so important, so vital a part of the lyric poem's meaning, in any worthy sense. "No poetic translation," says Hayward's reviewer, already quoted, "can give the rhythm and rhyme of the original; it can only substitute the rhythm and rhyme of the translator." One might just as well say "no prose translation can give the sense and spirit of the original; it can only substitute the sense and spirit of the words and phrases of the translator's language ;" and then, these two assertions balancing each other, there will remain in the metrical translator's favor, that he may come as near to giving both the letter and the spirit, as the effects of the Babel dispersion will allow... Continue reading book >>
Wikipedia – Johann Wolfgang von Goethe
Wikipedia – Faust; a Tragedy, Translated from the German of Goethe


"An SEM search for subsurface life -- developing a research model for l" by Andrea Lee DeStefano, Jill Caroline Ford et al.
An SEM search for subsurface life -- developing a research model for life on Mars.
The purpose of this project was to use a terrestrial model of subsurface life as an archetype for life on Mars. This Major Qualifying Project entailed a scanning electron microscopic search, with energy dispersive spectra analysis, of subsurface life in rock extracted from two South African gold mines. Several lines of evidence indicate the presence of biomarkers in the subsurface rock samples. This project was conducted at the Lyndon B. Johnson Space Center, along with NASA's Mars Meteorite Research Team.


text:
Sex Files Alien Erotica
Nymphomaniacs aliens roam the universe. Men and women, beautiful scientists looking for a remedy. And light-hearted, always beautiful, secret agents providing investigate as a demented and sexy version of Moulder and Skelly. The series "Sex Files: Alien Erotica" travels on these latitudes, but it also said that we are far from trivial and a handcrafted. Ok, everything leads to soft-core and the sex scenes are long, nudity in very large number, but the film tries and had a history and had a setting (and some special effect) not bad at all.
The first episode of this saga, starring a alien "mushroom" stuck close to a spacecraft on a mission and then take as"Invasion of the Body Snatchers" the features of the astronauts. The odor given off from from this creature leads all to an irrepressible desire to have sex.
The best idea of the whole story is that in reality the fungus hasn't ambitions of conquest, it wants only return to earth reunited with another fungus ( male) taken away by mistake from a previous mission. And they had sex happily. Between soft-core scenes, smaller than the following film and a sort of comedy brought by two agents.
"Sex Files: Alien Erotica" flow quietyl and is an happily watching, and making runs for the genre, big word, a masterpiece. Rolfe Kanefsky behind the camera performs his task with scrupulous activities, however, without inventing anything. The cast stands out the figure of Kira Reed and Gabriella Hall famous models and actresses to show sexy movies and soft core.


Welcome to Greek trashy hour on Birst Radio! For two hours, Iakovos Panagopoulos and Kyriakos Katsarakis deliver an original Greek show with popular Greek songs and casual talk. The spirit is going to be in high levels so we warn you that if you feel an urgent need to stand up from your couches and dance on your tables please fell free to do it….


There's nothing better than locally produced, genuinely fresh fruits and vegetables that are bursting with flavour. When they are also cheap fruits and vegetables as well, that's even more appealing! As convenient as popping down to the supermarket can be to get your groceries, when it comes to their fruit and veg, you're likely to find imported produce from overseas that may have potentially been in transportation and on the shelves for months. But it doesn't have to be that way. Big Watermelon is a fruit and vegetable wholesaler near Heathmont that provides residents, restaurants, workplaces and retailers with the freshest, locally grown cheap fruits and vegetables.
From everyday wholesale fruits and vegetables like apples, oranges, carrots and capsicums through to more exotic fare, Big Watermelon is the premier independent fruit and vegetable shop serving the people and businesses of Heathmont. Located in Wantirna South, 26 kilometres east of the CBD, we supply locally produced fruits and vegetables direct to the public as well as to businesses in the local area.
Click here to read about fruit and vegetables delivery near Heathmont.
Big Watermelon is open seven days a week from 7am to 6pm. Next time you want the best fresh fruits and vegetables, drive past your local supermarket and visit us to discover farm-fresh, juicy produce from truly local sources.


text:
package com.owera.xaps.shell.testperf;

public class City {
	private int percent;
	private String name;
	private int incLowerLimit;
	private int excUpperLimit;

	public City(String cityStr) {
		this.name = cityStr.trim().split("\\s+")[0].trim();
		this.percent = new Integer(cityStr.trim().split("\\s+")[1].trim());
	}

	public int getPercent() {
		return percent;
	}

	public void setPercent(int percent) {
		this.percent = percent;
	}

	public String getName() {
		return name;
	}

	public void setName(String name) {
		this.name = name;
	}

	public int getIncLowerLimit() {
		return incLowerLimit;
	}

	public void setIncLowerLimit(int incLowerLimit) {
		this.incLowerLimit = incLowerLimit;
	}

	public int getExcUpperLimit() {
		return excUpperLimit;
	}

	public void setExcUpperLimit(int excUpperLimit) {
		this.excUpperLimit = excUpperLimit;
	}

	public String toString() {
		return "\t" + name + " " + incLowerLimit + "-" + (excUpperLimit - 1);
	}
}

redpajama_set_name: RedPajamaGithub


VENTURES AFRICA – Nairobi recently emerged the smartest city in Africa, creating in the process an incentive for other continental cities to join the bandwagon. In a very recent development, the Government of the Republic of Rwanda has entered into an official agreement with Ericsson, a key Communications and Technology Services provider, to kick-start the smart Rwanda project.
The project will be a critical enabler of the Rwandan vision 2020 and its attendant mid-term economic development and poverty reduction (the EDPRS II) and the Information and Communications Technology (ICT) sector strategic plan for 2013 to 2018. The initiative is a government effort aimed at applying the power of ICT in the development agenda to transform the social and economic development of the country.
The deal is structured such that Ericsson will provide ICT infrastructure to help Rwanda achieve its ICT development vision, one village at a time.
"Ericsson will invest in ICT infrastructure and also implement the project. We are committed to helping other countries to build smart cities. We are happy to drive the African mission to Rwanda. We will deploy smart solutions for Rwanda smart city initiative. We are pushing to expand smart Rwanda to other countries. The focus is on education, health, agriculture, service sector, among others. We are also discussing with other African countries in the same project," revealed Fredrik Ledling, President of Ericsson Sub-Saharan Africa during the Mobile World Congress in Barcelona.
Jean Nsengimana, the Rwandan Minister for Youth and ICT expressed his optimism at the prospects of such a behemoth project especially with respect to the Vision 2020 agenda. According to him, the core areas to be covered in the project include smart education, smart healthcare, smart governance, smart business, smart agriculture and infrastructure, among others.
"Ericsson has been our partner in the roll out plan. Rwanda is steadily moving towards its vision of becoming an information-rich and knowledge-based economy and society and an ICT hub in the region. The key to the success of smart Rwanda is sustainability of all the country´s interventions. Our strategy will be to rely on the much needed private sector resources and capabilities," he said.
Smart cities are fast becoming the present-day ICT fad for metropolises around the globe. These cities leverage digital technologies to enhance performance and overall quality of life while reducing city-wide costs and resource consumption. The usual end result is a positive impact on sustainable economic growth, competitiveness, and shared prosperity.
The Algerian War, also known as the Algerian War of Independence or the Algerian Revolution (Berber: Tagrawla Tadzayrit; Arabic: الثورة الجزائرية Al-thawra Al-Jazaa'iriyya; French: Guerre d'Algérie or Révolution algérienne) was a war between France and the Algerian independence movements from 1954 to 1962, which led to Algeria gaining its independence from France. An important decolonization war, it was a complex conflict characterized by guerrilla warfare, maquis fighting, terrorism, the use of torture by both sides, and counter-terrorism operations. The conflict was also a civil war between loyalist Algerians supporting a French Algeria and their insurrectionist Algerian nationalist counterparts.
In 1961, President Charles de Gaulle decided to give up Algeria, although it was regarded as an integral part of France, after conducting a referendum showing huge support for Algerian independence. The planned withdrawal led to a state crisis, to various assassination attempts on de Gaulle, and some attempts of military coups. Most of the former were carried out by the Organisation de l'armée secrète (OAS), an underground organization formed mainly from French military personnel supporting a French Algeria, which committed a large number of bombings and murders in both Algeria and the homeland to stop the planned independence.
Upon independence, in 1962, 900,000 European-Algerians (Pieds-noirs) fled to France, in fear of the FLN's revenge, within a few months. The government was totally unprepared for the vast number of refugees, causing turmoil in France. The majority of Algerian Muslims who had worked for the French, were disarmed and left behind as the treaty between French and Algerian authorities declared that no actions could be taken against them. However, the Harkis in particular, having served as auxiliaries with the French army, were regarded as traitors by the FLN and between 50,000 and 150,000 Harkis and family members were murdered by the FLN or lynch-mobs, often after being abducted and tortured. About 91,000 managed to flee to France, some with help from their French officers acting against orders, and today they and their descendants form a significant part of the Algerian-French population.
The Angolan War of Independence (1961–1974) began as an uprising against forced cotton cultivation, and became a multi-faction struggle for the control of Portugal's Overseas Province of Angola among three nationalist movements and a separatist movement. The war ended when a leftist military coup in Lisbon in April 1974 overthrew Portugal's Estado Novo regime, and the new regime immediately stopped all military action in the African colonies, declaring its intention to grant them independence without delay.
Portugal's wars against independence guerrilla fighters in its 400-year-old African territories began in 1961 with Angola. In Mozambique, the conflict erupted in 1964 as a result of unrest and frustration amongst many indigenous Mozambican populations, who perceived foreign rule to be a form of exploitation and mistreatment, which served only to further Portuguese economic interests in the region. Many Mozambicans also resented Portugal's policies towards indigenous people, which resulted in discrimination, traditional lifestyle turning difficult for many Africans, and limited access to Portuguese-style education and skilled employment.
As successful self-determination movements spread throughout Africa after World War II, many Mozambicans became progressively nationalistic in outlook, and increasingly frustrated by the nation's continued subservience to foreign rule. For the other side, many enculturated indigenous Africans who were fully integrated into the Portugal-ruled social organization of Portuguese Mozambique, in particular those from the urban centres, reacted to the independentist claims with a mixture of discomfort and suspicion. The ethnic Portuguese of the territory, which included most of the ruling authorities, responded with increased military presence and fast-paced development projects.
A mass exile of Mozambique's political intelligentsia to neighbouring countries provided havens from which radical Mozambicans could plan actions and foment political unrest in their homeland. The formation of the Mozambican guerrilla organisation FRELIMO and the support of the Soviet Union, China, Cuba, Yugoslavia, Bulgaria, Tanzania, and Zambia through arms and advisers, led to the outbreak of violence that was to last over a decade.
From a military standpoint, the Portuguese regular army held the upper hand during the conflict against the independentist guerrilla forces. Nonetheless, Mozambique succeeded in achieving independence on June 25, 1975, after the coup d'état in Portugal known as the Carnation Revolution, thus ending 470 years of Portuguese colonial rule in the East African region. According to historians of the Revolution, the military coup in Portugal was in part fuelled by protests concerning the conduct of Portuguese troops in their treatment of some local Mozambican populace. The role of the growing communist influence over the group of Portuguese military insurgents who led the Lisbon's military coup, and, on the other hand, the pressure of the international community over the direction of the Portuguese Colonial War in general, were main causes for the final outcome.


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The Effect of Business Mathematics Instruction on Student Performance in Learning to Operate Office Calculating Machines.
Aina, Oluremi Raphael, "The Effect of Business Mathematics Instruction on Student Performance in Learning to Operate Office Calculating Machines." (1974). All NMU Master's Theses. 196.


Work has begun on an expansion of The Glenlivet distillery, reinforcing the recent success and bright future for the world's largest single malt Scotch whisky.
Chivas Brothers has forged ahead with its investment into enhancing the production facilities of The Glenlivet distillery to ensure that current and future demand for 'the single malt that started it all' continues to be met. Work officially began on the site on 2nd September, which will significantly increase capacity.
The news follows a strong set of financial results for the year ending in June 2015 for Chivas Brothers, announced last week, with the Scotch whisky and premium gin business of Pernod Ricard recording overall growth in net sales of +3%.
The Glenlivet recorded the standout achievement for Chivas Brothers with +11% net sales growth, a result of the brand's commitment to innovation and craftsmanship through launches such as Founder's Reserve, the extension of the Master Distiller's Reserve range and The Winchester Collection. The Glenlivet has successfully driven consumer recruitment and attracted Scotch connoisseurs to the brand, which has made it the largest contributor to the growth of the single malt category in the past five years (IWSR, 2014).
Today's announcement reinforces the brand's recent unrivalled global success selling over 1 million cases to become the world's No.1 single malt Scotch whisky brand. The Glenlivet is also spearheading growth for the entire Pernod Ricard Single Malt Scotch whisky portfolio, with the group's range becoming the Global No. 1.
Laurent Lacassagne, Chairman & CEO of Chivas Brothers, commented: "Today's first step towards an expansion at The Glenlivet distillery is an historic day for Chivas Brothers as we look to continue the brand's phenomenal triumphs across the past five years to reinforce our position as the world's No.1 single malt Scotch whisky."


text:
It is reported that the man being executed is 26 years old, and had been imprisoned when he was only 13 years old. (Screenshot)
Horrific video shows man hung by crane in Iran public execution
Staff writer, Al Arabiya English
Published: 16 September ,2018: 12:00 AM GST Updated: 20 May ,2020: 10:54 AM GST
Viewer discretion advised
Iranian social media accounts have shared a video showing a brutal execution of an old man being hanged while lifted with a crane before the eyes of the public.
Human rights activists who shared footage of the incident claimed that it took place on Friday in the city of Marvdasht, southern Iran.
Warning: Graphic content.
This isn't Syria or Mosul under ISIS rule. This is #Iran, forcing people to watch security forces executing a 26 years old man in public.
Executed person was sentenced to death when he was only 13.@amnestyusa @UNHumanRights @hrw @BBC @France24_en pic.twitter.com/GF462rGwQl
— Raman Ghavami (@Raman_Ghavami) September 14, 2018
It is reported that the man being executed is 26 years old, and had been imprisoned when he was only 13 years old.
The footage shows hundreds gathered to witness the execution, as women who are believed to be related to the man scream in the background, condemning the execution be carried in this manner.
The Iranian Human Rights Organization said there had been an increase in executions during the past few months, noting that 30 executions were carried in August only.
Amnesty International have previously said in its annual report that at least 507 people were executed in Iran during 2017.
Tehran prosecutor: Many arrested in Iran bazaar protests, may face execution
Several civilians who joined demonstrations at Iran's Tehran Bazaar have been arrested and will likely face trial, the Prosecutor General of ... Middle East
UN experts urge Iran to halt 'unlawful execution' of juvenile offender
Two UN rights experts urged Iran on Tuesday to halt the execution of a man scheduled to take place shortly following the end of Ramadan, after he was ... Middle East
Iran executes Sufi opposition member accused of running over police officers
Judicial sources in Iran said they upheld the death sentence of a Sufi opposition member Mohammad Reza Salas on Monday morning, after being accused ... Middle East
More than half of global executions carried out in Iran, says report
According to the latest report of the Amnesty International as reported in Iran Focus website, among all the recorded executions worldwide last year, ... Features


text:
REGINALD PEERS
Rank: Gunner
Regiment: 106th Siege Bty. Royal Garrison Artillery
Died of wounds Thursday 29th November 1917
County Memorial Chester
Commemorated\Buried Dozinghem Military Cemetery
Grave\Panel Ref: XV.E.3.
Reginald's Story.
Nantwich Guardian, Friday, December 14, 1917.
Died of Wounds.
GUNNER R. PEERS.
It has been officially notified that Gunner Reginald Peers, R.G.A., so of Mrs. Peers, Chapel Terrace, Chester and of the late Mr. Alfred Peers, blacksmith, of Commonhall Street, Chester, died of wounds on November 29th. Gunner Peers was married and leaves a widow and one boy. He formerly was a barman with Mr. George Barlow, Bridge Street. He was born in Chester and attended Grosvenor St. John's School. His father was one of the bellringers at the Cathedral, a position he had held for 28 years.
The Cheshire Roll of Honour would like to thank Nigel Meyrick and Mrs. C. Meyrick for the picture of Reginald.


Nice water reflection effect makes your image to live.
Inner effect core is optimized with C language, So this app should be lighter, and use little less battery, than only java versions. Because of this, works with quite old phones too.
This live wallpaper makes reflection from selected image to bottom of the screen, and it looks like the reflection is from water waves. There is one small default picture, (shown in example pictures) but you can choose your own image to background. Some pictures might look very funny, if those are difficult to think near water, but most of the pictures looks more living with this effect.


text:
Rangers: Club plan to ease Ryan Kent back into action after injury
By Jack Maleham
Ryan Kent may not be included in the Rangers starting line-up for the next month, according to a report from Football Insider.
The winger is coming back from injury and it is thought that the club have planned in detail how they will handle his return to first-team action.
Since joining on a permanent deal from Liverpool in the summer, Kent has endured a frustrating start to the campaign.
So far, the winger has managed to play just 41 minutes of first-team football, which came against Livingston back in September.
A hamstring injury has kept him out of action, but Steven Gerrard confirmed after their 5-0 win against Hamilton that they expect the player to be available after the international break.
However, Football Insider are reporting that the club will look to ease Kent back into action with a few substitute appearances before handing him a start.
Having broken down so quickly against Livingston, Gerrard and his staff are keen to ensure that does not happen again and want him to be 100% ready before playing 90 minutes.
Kent is an important player for Rangers, as shown in his performances on loan at the club last season.
The 22-year-old managed to provide six goals and six assists for the Ibrox club in 2018/19, and he will add even more creativity going forward.
However, the Gers have made an excellent start to the current campaign and have won seven of their opening eight matches in the league.
In that time they have had no issues in front of goal, and are the leading scorers in the division having already netted 26 times (via BBC Sport).
With that in mind, there is little point rushing Kent back. Yes, he is an excellent player, but the club are coping well without him so the priority has to be making sure he is fully fit and ready for action by the time they name him in the starting line-up.
Rangers fans, how important will Ryan Kent be once he returns from injury? And are the club doing the right thing in not rushing him back into the first team? Let us know your thoughts in the comments below…
Related Items:Rangers, Ryan Kent, Steven Gerrard
Rangers: Fans slam Ewan Murray tweet
Rangers: Fans perplexed by Richard Foster interview
Rangers: Scott Wright compared to Ryan Kent
Article title: Rangers: Club plan to ease Ryan Kent back into action after injury


Fast Image Viewer Free APK Latest Download For PC Windows Full Version.Fast Image Viewer Free APK Apps Full Version Download for PC.Descargar Fast Image Viewer Free APK Latest Version for PC,Ordenador portátil,ventanas.
Includes a fast and powerful file browser which displays a large thumbnail image and file details. Long press on the name for the option to share the image (correo electrónico, mms, etc.) or set it as the background wallpaper.
3.Abrir el emulador de Android para PC,Ordenador portátil,Tablet import the Fast Image Viewer Free APK file from your PC Into Android Emulator to install it.
4.Instalar Fast Image Viewer Free APK Aplicaciones para PC Windows.Now se puede jugar Fast Image Viewer Free APK en PC.


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sessions for managers and directors.
We're the marketing strategy company that helped Crimsafe get a 30% increase in sales turnover from November 2009 that continued month-by-month.
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And DJ Builders turned their marketing around to get 30 leads a week where their old marketing got just 5. They defied the Housing downturn.
We're a marketing strategy company that develops break-through strategies, creates marketing collateral and puts it into action to grow your company faster. As seen on SkyNews and in Australian Business Solutions magazine.
We're the only company that takes direct responsibility for building a stronger strategy and successfully implementing it with you.
Just like Crimsafe, Loctite, DJ Builders, Pool Pro and many more clients, you might already have marketing and sales activities. But they're not working as well as you'd like. So you're looking for a marketing company to help you get a breakthrough strategy or a powerful campaign.
We discover what your market's unmet needs are. We discover the hidden weaknesses your competitors have. And we identify your company's strengths and weaknesses. From these, we build a breakthrough strategy.
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Need a Quick Fix TODAY?
Our Marketing Workshops and phone consults are perhaps the most high-return form of consulting available in Australia. In as little as 2 hours, you can have advice on specific issues you want a Marketer's input on. And within a half-day workshop, you can have a bundle of ideas for growth to work on.
We've served almost every sector in Australia… more than 375 companies… in 13 years. We've worked in your sector before, too. But it's the process we take to uncovering hidden assets and building the right strategy that is most impactful. We get of our biggest breakthroughs for clients when we help them look at their company freshly.
Listing them would take time so here are a few well known companies we've worked with. We also have testimonials from customers regarding their experiences with us.


The next meeting of the SAE G-11 Reliability, Maintainability, Supportability, and Logistics Division (including the G-11SW Committe) will be held March 6-6, 2006 in Hampton, Virginia, U.S.A.. This meeting will be hosted by NASA Langley Research Center.
The meeting will take place in Room #137.
Below is a listing of hotels in the Hampton, Virginia area. To obtain this list click here.
The best airports to fly into are Norfolk International (ORF) or Newport News/Williamsburg (PHF).
How To Register for the Conference. Register on-line at Online Preregistration Form . Please contact Ms. Kerri Rohall at +1-757-325-6700 or kerrir@sae.org if you have any questions.
Software-supportability.org highly recommends your attendance to this event. The SAE G-11SW Software Committee is one of the world leading committees in the field of software reliability and *only* standarization committee addressing software supportability!
Are you aware of any upcoming events in the field? Please contact us at webmaster@software-supportability.org.


Hall & Partners today announced that its integrated data platform, The Hub, has won the NGMR Innovative Research Deployment Award for 2015.
In addition, The Hub's founder, Oliver Hayward, was named a finalist in the NGMR Individual Achievement Award—recognised for demonstrating outstanding leadership as a change agent.
The Hub is a pioneering data integration and publishing platform, which enables Insights professionals to become brand journalists, turning data and insights into memorable and actionable, bite-sized stories. The Hub helps clients make the most of all their data, with the ability for decision-makers to dig into multiple data sets directly from the stories, using intuitive, dynamic visualisations, all on their tablets.


text:
cd /gq-parse-server &&\
npm start


This failure happens because a "tcp window full" message is sent, and then Nexus/Jetty tries to negotiate a new TCP window size, but for some reason the deployer won't accept anything sent.
As far as we can tell this is a bug in the JDK URL classes Ivy uses by default when publishing artifacts. The solution is to configure Ivy to use HttpClient for publishing.


What was/is European security in the context of the Cold War? How was and is it conceived? What role did "non-powers" play in European security, and how did they help define it? These were the main questions discussed during the conference held by the C²DH in March 2017. This edited volume brings together the final, peer-reviewed contributions of the participants, and brings them together in a common publication.


Repair and restoration work can be as simple as cleaning and re-rigging, or it could involve re-building broken or missing parts! I can give you a reasonable estimate by viewing your model or by looking at detailed photographs.
I'm always so eager to start a new project that I've been remiss in taking "before" photos. Check back soon for more photos on this page!


text:
\section{\label{sec:1}Introduction}

Quantum electrodynamics predicts that an excited atom, interacting with the quantum electromagnetic field in the vacuum state, spontaneously decays to its ground state by emitting a photon. The emission probability for unit time is found to be
\begin{eqnarray}
\label{eq:1}
A=\frac 4 3\frac{\omega_{eg}^3 \mid\boldsymbol\mu^{eg}\mid^2}{\hbar c^3}\, ,
\end{eqnarray}
where $\boldsymbol\mu^{eg}$ is the matrix element of the atomic dipole moment operator between the atomic excited and ground states, and $\omega_{eg}$ is the transition frequency between the two atomic levels \cite{dirac}.  This result can be generalized to the case of $N$ atoms
incoherently coupled to the quantum electromagnetic field: in this case, the $N$ atoms decay independently, and the intensity of the emitted radiation is proportional to $N$.
Dicke in $1954$ \cite{dicke54} showed that this conclusion is not valid in general: when N identical atoms are confined within a volume $V\ll\lambda^3$, where $\lambda$ is the wavelength of emitted radiation, the assumption of uncorrelated emitters is no longer valid and a closer reconsideration of the problem is necessary. It was shown that an ensemble of atoms coherently coupled to the quantum electromagnetic field, acts as a single quantum emitter, with a decay rate equal to $N A$, and an intensity of the emitted radiation proportional to $N^{2}$ \cite{persico,benedict}. This enhanced single-photon emission is known as \textit{superradiance}, and its physical origin is in the correlation (symmetric state) between the atomic dipoles, leading to a constructive interference in the emission of radiation.

The counterpart of superradiance is the so-called \textit{subradiance} \cite{dicke54,gross}, that occurs when the ensemble of atoms is prepared in a correlated antisymmetric state. In this case, a suppression of the emission intensity occurs, and the decay is totally inhibited. Contrarily to superradiance, subradiance arises from anticorrelations between the atomic dipoles, leading to a destructive interference in the emission of radiation. While superradiant states are affected by decoherence, subradiant states are free-decoherence robust states, and for these reasons they are considered promising for realization of high-performance quantum processors in quantum information technologies~\cite{petrosyan}.

Superradiance and subradiance have been investigated in a variety of systems, including atoms~\cite{pavolini,braggio}, trapped ions~\cite{devoe}, quantum dots~\cite{scheibner} coupled to various environments, such as cavities~\cite{temnov,pan}, waveguides~\cite{martin-cano,fleury}, and photonic crystals~\cite{ghhmypk15}.

Very recently, the influence of a perfect reflector on the cooperative spontaneous emission process of two atoms located nearby has been discussed~\cite{palacino}.
The effect of a surface or a structured environment, or of an external static electric field on other radiative processes, such as dispersion or resonance interactions between atoms, have been recently studied~\cite{incardone, notararigo,fiscelli, fiscelli1,shahmoon,shahmoon1,fiscelli2}.

Most of these studies concern with a static environment.
In this paper, we consider a different and more general situation, specifically we discuss the influence of a dynamical (i.e. time-dependent) environment on the cooperative emission of two correlated identical atoms located nearby.

Generally speaking, a dynamical environment can be realized by changing periodically the magneto-dielectric properties of the material or by a mechanical motion of macroscopic objects, such as a reflecting mirror or the cavity walls.
These systems, for example vibrating cavities or oscillating mirrors, have been extensively explored in connection with the dynamical Casimir and Casimir-Polder effect~\cite{dodonov, braggio1, dodonov1,antezza}. Also, dynamical cavities have been simulated in circuit QED~\cite{bosco}.

Recent investigations have shown that the presence of a dynamical environment can give additional possibilities (not present in the case of a static environment) to manipulate and control radiative properties of atoms or molecules coupled to a quantum field.
For example the spontaneous emission of an excited atom located near a perfectly reflecting plate that oscillates adiabatically has been recently discussed~\cite{glaetze, ferreri}, and it has been shown that the motion of the mirror significantly affects the atomic decay rate, as well as the spectrum of the emitted radiation, exhibiting the presence of two lateral and almost symmetrical peaks, not present in the case of a static boundary~\cite{ferreri}. Similar results
were also obtained in the case of an excited atom embedded in a dynamical photonic crystal, when its transition frequency is close to the photonic band edge of the photonic crystal~\cite{calajo}. Here, the presence of a time-modulated photonic band-gap gives rise to two lateral peaks in the spectrum of radiation emitted. These lateral peaks are asymmetric due to the rapidly varying local density of states at the edge of the gap.
Furthermore, the time-dependent resonance interaction between atoms, the dynamical Casimir-Polder interaction between atoms or between an atom and a mirror, have been investigated during the dynamical self-dressing process of the system, starting from a nonequilibrium configuration; it has been shown that forces usually attractive can become repulsive in non-equilibrium situations~\cite{rizzuto,vasile,messina1,armata,barcellona, barcellona1,haakh}. These results show the striking potentialities of time-dependent environments and nonequilibrium configurations for manipulating a variety of radiative processes.

In this paper, we consider two identical atoms, one in the ground state and the other in the excited state, prepared in a correlated {\em Bell}-type state (symmetric or antisymmetric), while the electromagnetic field is in its vacuum state. In the Dicke model, these states are the well-known superradiant and subradiant states, respectively~\cite{dicke54}.
We assume that the two atoms are located near a perfectly reflecting mirror that oscillates adiabatically along a prescribed trajectory, and
we investigate the effects of the mirror's motion on the cooperative spontaneous decay, the spectrum emitted by the two quantum emitters, and their decay rate.
We suppose that the reflecting plate oscillates adiabatically along a sinusoidal trajectory. Under these assumptions, the field mode functions, satisfying the boundary conditions at the mirror surface at any time, are time-dependent.
Using time-dependent perturbation theory, we investigate the spectrum of the emitted radiation, and the cooperative decay rate of the two-atom system.
We show that the adiabatic motion of the mirror modifies the physical features of the spectrum of the radiation emitted. In particular, we find the presence of two symmetric side peaks in the spectrum, not present in the case of a static mirror, and separated by the central peak by the mirror's oscillation frequency.
We also evaluate the transition rate to the collective ground state of the two-atom system, in both cases of the superradiant (symmetric) and subradiant (antisymmetric) state, and show that it depends on the interatomic separation and the time-dependent atom-plate distances.
We also find that the motion of the mirror can cause a significant enhancement or suppression of superradiance of the two quantum emitters, depending from the specific configuration of the system, with respect to the cases of a mirror at rest or atoms in the unbounded space. These results show how a dynamical environment can influence the physical features of the superradiant and subradiant emission by the two correlated atoms, that can be enhanced or inhibited compared to the case of atoms in the vacuum space or near a static boundary.
In general, this further confirms that a dynamical (i.e. time-modulated) environment can give new possibilities to control, manipulate and also activate or inhibit radiative processes of atoms and molecules nearby, such as the cooperative spontaneous emission by two correlated atoms. It suggests that also other radiative processes, such as the resonance interaction and the energy transfer between atoms or molecules, can be tailored exploiting a dynamical environment.

The paper is organized as follows. In Section \ref{sec:2}, we introduce our system, and investigate the spectrum of the radiation emitted by the two-atom system, and discuss its main physical features (some technical points on our model are in the Appendix). In Section \ref{sec:3} we investigate the collective decay rate of the two quantum emitters in the presence of the oscillating mirror. Section \ref{sec:4} is devoted to our concluding remarks.

\section{\label{sec:2} Spectrum of the radiation emitted by two entangled atoms near an oscillating mirror}

Let us consider two atoms, labeled as A and B, located in the half-space $z>0$ near an infinite perfectly conducting plate, modeled as two-level systems with atomic transition frequency $\omega_0$, and interacting with the electromagnetic field in the vacuum state.
We suppose that the mirror oscillates with an angular frequency $\omega_p$, along the $z$ direction with the trajectory
$a(t) = a \sin(\omega_p t)$, where $a$ is the oscillation amplitude of the plate around its average position $z=0$.

Let us suppose that the two identical two-level atoms are initially prepared in a symmetric or antisymmetric entangled state, i.e.
\begin{eqnarray}
\label{eq:2}
\vert\phi\rangle_{\pm}=\frac{1}{\sqrt{2}}(\vert e_A,g_B\rangle\pm\vert g_A, e_B\rangle)\, ,
\end{eqnarray}
and that the quantum field is in its vacuum state. Thus, the initial state of the system at time $t=0$ is
\begin{eqnarray}
\label{eq:3}
\vert i \rangle_{\pm}=\vert\phi\rangle_{\pm}\vert vac\rangle\, .
\end{eqnarray}
The sign $\pm$ in \eqref{eq:2} refers to the symmetric or antisymmetric state respectively, $\vert vac\rangle$ is the vacuum state of the electromagnetic field, while $\vert e_{A(B)}\rangle$ ($\vert g_{A(B)}\rangle$) indicates the excited (ground) state of atom $A (B)$. In the states \eqref{eq:2} the excitation is delocalized between the two atoms. In the Dicke model, these states are the so-called superradiant and subradiant states, respectively.
They can be realized experimentally with actual techniques~\cite{filipp,mlynek}.
Symmetric (antisymmetric) states are also at the origin of the resonant interaction energy, which is a second-order interaction between correlated atoms~\cite{craig}.

Our physical system is displayed in Figure~\ref{fig:1}.

\begin{figure}[!htbp]
\centering\includegraphics[width=8.2 cm]{fig1}
\caption{Sketch of the system: two atoms, modeled as two-level systems with transition frequency $\omega_0$, are placed in front of an oscillating mirror. The atomic dipole moment of each atom can be oriented parallel or perpendicular to the oscillating reflecting plate.}
\label{fig:1}
\end{figure}

We assume that the oscillation frequency $\omega_p$ of the plate is much smaller than the atomic transition frequency $\omega_0$ of both atoms, and of the inverse of the time taken by the photon emitted by one of the two atoms, to reach the other atom after reflection on the mirror ($\omega_p\ll c/r_A, c/r_B, c/(r_A+r_B)$, where $r_{A/B}$ is the average atom-plate distance of each atom from the mirror). Under these assumptions, we can neglect real photons emission by dynamical Casimir effect, and investigate the collective spontaneous emission by the two correlated atoms in the adiabatic approximation. These assumptions are fully verified by typical values of the relevant parameters of the system, for example $\omega_p \sim 10^9 \,$s$^{-1}$, $\omega_0 \sim 10^{15} \,$s$^{-1}$, and an atom-plate average distance of the order of $10^{-6}\,$m, achievable in the laboratory.
We stress that such a system is experimentally feasible, using a dynamical mirror, that is a slab of semiconductor material whose dielectric properties are modulated in time for simulating the oscillating mirror~\cite{braggio1, antezza}, and keeping the atoms at a fixed position exploting atomic trapping techniques~\cite{wieman}.

We write the Hamiltonian of our system in the Coulomb gauge and in the multipolar coupling scheme, within the dipole approximation~\cite{compagno,craig,salam,passante18}:
\begin{equation}
\label{eq:4}
H=\hbar\omega_0 (S^A_z+S^B_z)+ \sum_{{\bf k}j}\hbar{\omega_k} a^{\dag}_{{\bf k}j}a_{{\bf k}j}+H_I ,
\end{equation}
where $S_z=\frac{1}{2}(\vert e\rangle \langle e \vert - \vert g\rangle \langle g \vert)$ is the pseudospin atomic operator, $a_{{\bf k}j}$ ($a^{\dag}_{{\bf k}j}$) are the bosonic annihilation (creation) operators for photons with wave vector $\bm{k}$ and polarization $j$, and $H_I$ is the interaction Hamiltonian, given by

\begin{equation}
\label{eq:5}
H_I = -(S_+^A+S_-^A)\boldsymbol\mu_A^{eg}\cdot{\bf E}({\mathbf r}_A)-(S_+^B+S_-^B)\boldsymbol\mu_B^{eg}\cdot{\bf E}({\mathbf r}_B).
\end{equation}

Here,
$S_+=\vert e \rangle \langle g \vert$, $S_-=\vert g \rangle \langle e \vert$ are atomic pseudospin operators, and
$\boldsymbol\mu_{A(B)}^{eg}= \langle e_{A(B)} \vert \hat{\boldsymbol\mu}_{A(B)}\vert g_{A(B)}\rangle$ are the matrix elements, assumed real, of the atomic dipole moment operator $\hat{\boldsymbol\mu}_{A(B)}$ of atom $A$ ($B$) between its excited and ground state.
${\bf E}({\mathbf r}_{A(B)})$ is the electric field operator at the atomic position ${\mathbf r}_{A(B)}$; it includes a time dependence as a consequence of the motion of the conducting wall, as discussed in detail in the Appendix.

The orientation of the atomic dipole moment is determined by the specific atomic states $\lvert e \rangle$ and $\lvert g \rangle$ taken in our two-level model. For example, if the excited state is one of the three degenerate states with $n=2, \, l=1, \, m=0,\pm 1$ of the hydrogen atom, and the ground state is the state with $n=1, \, l=0, \, m=0$ ($n$ is the principal quantum number, $l$ the orbital quantum number, and $m$ the magnetic quantum number), then the excited state with $m=0$ gives a dipole matrix element along $z$ (perpendicular to the wall), while specific linear combinations of the states with $m=1$ and $m=-1$ give a dipole along $x$ or $y$, that is parallel to the wall.

In general, the presence of time-dependent boundary conditions leads to introducing new creation and annihilation field operators, related to the old ones by a Bogoliubov transformation~\cite{dodonov}, and to time-dependent mode functions, satisfying the appropriate time-dependent boundary conditions.
However, in the present case of an adiabatic motion of the mirror as defined above, the field operators instantaneously follow the mirror's motion, and the creation and annihilation operators are the same of the static-wall case; also, we can set the usual boundary conditions for the electromagnetic field in the reference where the wall is instantaneously at rest, and then go back to the laboratory frame by the appropriate time-dependent space translation. Thus, the field annihilation and creation operators remain the same as in the static case, and the mirror's motion is entirely included in the field modes $(\omega_pa/c \ll 1)$.
The expression for the field operator appearing in \eqref{eq:5} with the adiabatically moving mirror, as well as the instantaneous field modes and relevant expressions for the sum over polarizations, are discussed in the Appendix.

Thus, the time dependence of the interaction Hamiltonian will be made explicit in the mode functions only (see the Appendix), while, as mentioned, the field annihilation and creation operators are the same as in the static case; in other words, in our adiabatic approximation, the atoms locally interact with the vacuum field fluctuations that instantaneously follow the motion of the mirror. In general, in dealing with our system, we can adopt two different points of view: with respect to the laboratory frame, where both atoms are at rest and the plate oscillates along a prescribed trajectory, or in the reference frame comoving with the mirror.
In this paper, we will adopt the laboratory frame.
Taking into account our hypothesis of an adiabatic motion of the mirror, the field vacuum state in our initial state \eqref{eq:3}, at $t=0$, is that relative to the instantaneous position of the mirror at that time, and it is independent of its previous motion (in fact, nonadiabatic effects such as photon emission by dynamical Casimir effect, or atomic excitation by dynamical Casimir-Polder effect \cite{antezza}, are negligible in our hypothesis). Mathematically, it is defined by $a_{{\bf k}j} \vert vac \rangle =0$, where the annihilation operator $a_{{\bf k}j}$ does not depend from time, because all time dependence relative to the wall's motion is embedded in the field modes.

Using the interaction Hamiltonian \eqref{eq:5}, a straightforward application of first-order time-dependent perturbations theory yields the transition amplitude from the initial entangled state \eqref{eq:3} to the state $\vert g_A,e_B,1_{{\bf k} ,j} \rangle$ (both atoms in their ground state, and one photon emitted in the mode $({\bf k} ,j))$
\begin{eqnarray}
\label{trans-ampl}
c({\bf k} j,t) &=& \sqrt{\frac {\pi ck}{\hbar V}} \int_0^t dt' e^{i({\omega_k} -\omega_0 )t'}  \nonumber \\
&\ & \times  \left[\boldsymbol\mu_A^{eg} \cdot {\bf E}({\mathbf r}_A,t') \pm \boldsymbol\mu_B^{eg} \cdot{\bf E}({\mathbf r}_B,t') \right] ,
\end{eqnarray}
where the $\pm$ sign refers to the superradiant or subradiant state of Eq.~\eqref{eq:2}.

The probability that the system, initially prepared in the correlated state \eqref{eq:3}, decays at time $t$ to the collective atomic ground-state, emitting a photon with wavevector ${{\bf k}}$ and polarization $j$, is then given by

\begin{widetext}
\begin{eqnarray}
\label{eq:7}
&\ &\lvert c({\bf k} j,t)\rvert^2 = \frac{\pi c k}{\hbar V}\int_0^{t}\int_0^{t}dt^\prime dt^{\prime\prime} \Big\{\boldsymbol\mu_A^{eg}\cdot{\bf f}_{{\bf k} j}({\mathbf r}_A,t^\prime)\boldsymbol\mu_A^{eg}\cdot{\bf f}_{{\bf k} j}({\mathbf r}_A,t^{\prime\prime})+\boldsymbol\mu_B^{eg}\cdot{\bf f}_{{\bf k} j}({\mathbf r}_B,t^\prime )\boldsymbol\mu_B^{eg}\cdot{\bf f}_{{\bf k} j}({\mathbf r}_B,t^{\prime\prime} )\nonumber\\
&\ & \ \ \pm \Big[\boldsymbol\mu_A^{eg}\cdot{\bf f}_{{\bf k} j}({\mathbf r}_A,t^\prime )\boldsymbol\mu_B^{eg}\cdot{\bf f}_{{\bf k} j}({\mathbf r}_B,t^{\prime\prime} )+\boldsymbol\mu_A^{eg}\cdot{\bf f}_{{\bf k} j}({\mathbf r}_A,t^{\prime\prime} )\boldsymbol\mu_B^{eg}\cdot{\bf f}_{{\bf k} j}({\mathbf r}_B,t^\prime )\Big]\Big\} e^{i({\omega_k}-\omega_0)(t^{\prime\prime}-t^\prime)} .
\end{eqnarray}
\end{widetext}

The first two terms in the right-hand side of Eq.~\eqref{eq:7} are related to the probability that each atom independently decays by emitting a photon; on the contrary, the contribution inside the square bracket is an {\em interference} term, and it is responsible of the superradiant or subradiant behavior of the two-atom system.

From Eq.~\eqref{eq:7} we can obtain the frequency spectrum of the radiation emitted by the two
atoms, that is the emission probability for unit frequency, by taking the sum over polarization and the integration over the directions of ${\bf k}$ as

\begin{equation}
\label{eq:8}
P({\omega_k},t)=\frac{V}{(2\pi)^3} \frac {{\omega_k}^2}{c^3} \int \! d\Omega \sum_j \lvert c({\bf k} j,t)\rvert^2 ,
\end{equation}

where $V$ is the quantization volume, and $\Omega$ the solid angle.
The integration over the directions of ${\bf k}$ that we will explicitly perform in the following is on the full $4\pi$ solid angle, because our field modes, given in the Appendix, allow positive and negative values of the components of ${\bf k}$.

We perform the sum over polarizations $j=1,2$, using the relation \eqref{eq:9} given in the Appendix, that extends to our adiabatic dynamical case the expression obtained in \cite{power82} for the static case. For convenience, we report here this relation
\begin{eqnarray}
\label{eq:9a}
&\ & \int \! d\Omega \sum_j [{\bf f}_{{\bf k} j}({\mathbf r}_u,t^\prime )]_\ell[{\bf f}_{{\bf k} j}({\mathbf r}_v,t^{\prime\prime} )]_m\nonumber\\
&\rightarrow& \int \! d\Omega \, \Re \Big\{(\delta_{\ell m}-{\hat {\bf k}_\ell}{\hat {\bf k}_m})e^{i{\bf k}\cdot({\mathbf r}_u-{\mathbf r}_v)}\nonumber\\
&\ & -\sigma_{\ell p}(\delta_{p m}-{\hat {\bf k}_p}{\hat {\bf k}_m})e^{i{\bf k}\cdot({\mathbf r}_u(t^\prime)-\sigma{\mathbf r}_v(t^{\prime\prime}))} \Big\}\, ,
\end{eqnarray}
where $\Re$ indicates the real part.

We stress that the relation \eqref{eq:9a} is valid only in our adiabatic approximation in the laboratory frame, that is when the electromagnetic field operators instantaneously follow the motion of the plate.
The first term in \eqref{eq:9a} is a free-space contribution,  and it is time-independent because the two atoms are fixed in space. On the contrary, the second term takes into account the presence of the oscillating mirror through the reflection matrix $\sigma = \text{diag}(1,1,-1)$ introduced in (\ref{eq:10}), and, in our adiabatic approximation, depends on the instantaneous time-dependent atom-mirror and atom-image distances (see the presence of the $\sigma$ reflection matrix).

The second term in Eq. \eqref{eq:9a} can be written as
\begin{equation}
\label{eq:11}
e^{i{\bf k}\cdot({\mathbf r}_u(t^\prime)-\sigma{\mathbf r}_v(t^{\prime\prime}))}=e^{i{\bf k}\cdot\bar{{\mathbf R}}_{uv}-{i{\bf k}\cdot\bf a}[\sin(\omega_p t^\prime)+\sin(\omega_p t^{\prime\prime})]} ,
\end{equation}
where $\bar{{\mathbf R}}_{uv}={\mathbf r}_u-\sigma{\mathbf r}_v$.
For a single atom, say $A$, $u=v=A$, and $\bar{{\mathbf R}}_{A}={\mathbf r}_A-\sigma{\mathbf r}_A$ represents the distance of atom $A$ from its image through the mirror; on the other hand, $\bar{{\mathbf R}}_{AB}={\mathbf r}_A-\sigma{\mathbf r}_B$, is the distance of one atom (say $A$) from the image of the other atom (say $B$).
For small oscillation amplitudes, such that $a\ll R_{A(B)},\bar{R}_{A(B)},\bar{R}_{AB}$, we can perform a series expansion of the exponential function in \eqref{eq:11} in powers of $a$, obtaining
\begin{eqnarray}
\label{eq:12}
&\ &e^{i{\bf k}\cdot({\mathbf r}_u(t^\prime )-\sigma{\mathbf r}_v(t^{\prime\prime} ))}\simeq e^{i{\bf k}\cdot\bar{{\mathbf R}}_{uv}}\biggl[1- i ({\bf k}\cdot\hat{\bf n}) a \nonumber\\
&\ &\times (\sin(\omega_p t^\prime)+\sin(\omega_p t^{\prime\prime})) - \frac 1 2 ({\bf k}\cdot\hat{\bf n})^2 a^2\nonumber\\
&\ &\times (\sin(\omega_p t^\prime)+\sin(\omega_p t^{\prime\prime}))^2+....\bigg]\, ,
\end{eqnarray}
where $\hat{\bf n}=(0,0,1)$ is the unit vector orthogonal to the oscillating plate.
We can now substitute the relations \eqref{eq:12} and \eqref{eq:9a} into \eqref{eq:7}, and integrate over time. Taking into account only terms up to the second order in the oscillation amplitude $a$, after some algebra we get

\begin{eqnarray}
\label{eq:13}
\int \! d\Omega \sum_j \lvert c({\bf k} j,t)\rvert^2 &\simeq&
g_A(\omega_k,t) + g_B(\omega_k,t)
\nonumber\\
&\ & \pm g_{AB}(\omega_k,t)
\end{eqnarray}

where
\begin{widetext}
\begin{eqnarray}
\label{eq:14}
&\ &
g_{A(B)}(\omega_k,t) =
\frac{\pi c k}{\hbar V}(\boldsymbol\mu_{A(B)}^{eg})_{\ell}(\boldsymbol\mu_{A(B)}^{eg})_{m}
 \Re \int \! d\Omega
\Big[
(\delta_{\ell m}-{\hat {\bf k}_\ell}{\hat {\bf k}_m}) h_0(\omega_k-\omega_0,t) - \sigma_{\ell p}(\delta_{p m}-{\hat {\bf k}_p}{\hat {\bf k}_m})e^{i{\bf k}\cdot{\bar{\mathbf R}}_{A(B)}}  \nonumber\\
&\ & \times \Big( h_0({\omega_k}-\omega_0,t) - i ({\bf k}\cdot\hat{\bf n}) a h_1({\omega_k}-\omega_0,\omega_p,t) - ({\bf k}\cdot\hat{\bf n})^2 \frac{a^2}{2} (h_2({\omega_k}-\omega_0,\omega_p,t)+h_3({\omega_k}-\omega_0,\omega_p,t)) \Big) \Big]
\end{eqnarray}
\end{widetext}
are the single-atom contributions ($\Re$ indicates the real part), and
\begin{widetext}
\begin{eqnarray}
\label{eq:15}
&\ &
g_{AB}(\omega_k,t) = \frac{4\pi c k}{\hbar V}(\boldsymbol\mu_{A}^{eg})_{\ell}(\boldsymbol\mu_{B}^{eg})_{m} \Re \int \! d\Omega
\Big[(\delta_{\ell m}-{\hat {\bf k}_\ell}{\hat {\bf k}_m})e^{i{\bf k}\cdot{{\mathbf R}}_{AB}} h_0(\omega_k-\omega_0,t) - \sigma_{\ell p}(\delta_{p m}-{\hat {\bf k}_p}{\hat {\bf k}_m})e^{i{\bf k}\cdot{\bar{\mathbf R}}_{AB}}
\nonumber\\
&\ &\times \Big( h_0({\omega_k}-\omega_0,t)- i ({\bf k}\cdot\hat{\bf n}) a\, h_1({\omega_k}-\omega_0,\omega_p,t) - ({\bf k}\cdot\hat{\bf n})^2 \frac{a^2}{2} (h_2({\omega_k}-\omega_0,\omega_p,t)+h_3({\omega_k}-\omega_0,\omega_p,t))\Big) \big] .
\end{eqnarray}
\end{widetext}
is the {\em interference} term, yielding the cooperative effects. In the expressions \eqref{eq:14} and \eqref{eq:15}, we have introduced the following functions

\begin{eqnarray}
&\ & h_0({\omega_k}-\omega_0,t)=\frac{\sin^2(({\omega_k}-\omega_0)t/2)}{(({\omega_k}-\omega_0)/2)^2} ,
\label{eq:16}
\end{eqnarray}

\begin{widetext}
\begin{eqnarray}
\label{eq:17}
&\ &h_1({\omega_k} -\omega_0,\omega_p,t)=\sin(\omega_p t/2)\frac{\sin[({\omega_k} -\omega_0 )t/2]}{({\omega_k} -\omega_0 )/2}
\left(\frac{\sin[({\omega_k} -\omega_0 +\omega_p)t/2]}{({\omega_k} -\omega_0 +\omega_p)/2}
+\frac{\sin[({\omega_k} -\omega_0 -\omega_p)t/2]}{({\omega_k} -\omega_0 -\omega_p)/2}\right) ,
\end{eqnarray}

\begin{eqnarray}
\label{eq:18}
h_2({\omega_k} -\omega_0,\omega_p,t)&=& \frac{\sin^2[({\omega_k} -\omega_0 +\omega_p)t/2])}{({\omega_k} -\omega_0 +\omega_p)^2/2}+\frac{\sin^2[({\omega_k} -\omega_0-\omega_p)t/2]}{({\omega_k} -\omega_0 -\omega_p)^2/2} -\cos (\omega_p t) \nonumber \\
&\ & \times \frac {\sin[({\omega_k} -\omega_0 +\omega_p)t/2] \sin [({\omega_k} -\omega_0 -\omega_p)t/2)]}{({\omega_k} -\omega_0 +\omega_p)({\omega_k} -\omega_0 -\omega_p)/4} ,
\end{eqnarray}

\begin{eqnarray}
\label{eq:19}
h_3({\omega_k} -\omega_0,\omega_p,t) &=& \frac{\sin^2[({\omega_k} -\omega_0 ) t/2]}{[({\omega_k} -\omega_0 )/2]^2}
-2\cos (\omega_p t) \frac {\sin [({\omega_k} -\omega_0) t/2]}{{\omega_k} -\omega_0}\left( \frac {\sin [({\omega_k} -\omega_0 +2\omega_p)t/2]}{{\omega_k} -\omega_0 +2\omega_p}\right.\nonumber\\
&\ &\left. + \frac{\sin [({\omega_k} -\omega_0 -2\omega_p)t/2]}{{\omega_k} -\omega_0 -2\omega_p} \right) .
\end{eqnarray}
\end{widetext}

These functions give the behaviour of the emitted spectrum by the two-atom system, as a function of the mirror's oscillation frequency $\omega_p$ and the atomic transition frequency $\omega_0$. They are responsible of the qualitative features and changes (with respect to the fixed-mirror case) of the spectrum of the radiation emitted, due to the motion of the boundary. In fact, inspection of \eqref{eq:16}-\eqref{eq:19} clearly shows that, in addition to the usual central peak at ${\omega_k}=\omega_0$ (present also in the case of a static mirror), new lateral peaks at ${\omega_k}=\omega_0 \pm \omega_p$ appear in the spectrum, due to the presence of energy denominators as ${\omega_k} -\omega_0 \pm \omega_p$ in Eqs.~(\ref{eq:17}-\ref{eq:19}). These contributions are clearly related to the motion of the mirror, and vanish in the limit of a static boundary, namely when $a$ and/or $\omega_p$ vanish.

Substituting Eqs. (\ref{eq:13}-\ref{eq:15}) into (\ref{eq:8}), and separating the terms according to the order of the plate's oscillation amplitude $a$, some straightforward algebra finally yields the expression of the emission spectrum in the form

\begin{equation}
\label{eq:21}
P({\omega_k},t)=P^{(0)}({\omega_k},t)+P^{(1)}({\omega_k},t)+P^{(2)}({\omega_k},t) ,
\end{equation}
where $P^{(0)}({\omega_k},t)$ is the $0$-th order contribution, while $P^{(1)}({\omega_k},t)$ and
$P^{(2)}({\omega_k},t)$ give respectively the first- and second-order (in the mirror's oscillation amplitude $a$) modification to the spectrum consequent to the adiabatic motion of the mirror. Such contributions are
\begin{widetext}
\begin{eqnarray}
\label{eq:22}
P^{(0)}({\omega_k},t) &=&
\frac{ k^3 }{2\pi\hbar}
\sum_{u=A}^{B}(\boldsymbol\mu_u^{eg})_{\ell}(\boldsymbol\mu_u^{eg})_{m}\biggl[\frac 2 3 \delta_{\ell m}-\sigma_{\ell p}F_{m p}^{\bar{R}_u}\frac{\sin(k\bar{R}_u)}{k^3\bar{R}_u}\biggr]\frac{\sin^2(({\omega_k}-\omega_0)t/2)}{(({\omega_k}-\omega_0)/2)^2}\nonumber\\
&\ & \pm\frac{c k^3 }{\pi\hbar}(\boldsymbol\mu_A^{eg})_{\ell}(\boldsymbol\mu_B^{eg})_{m}\biggl[F_{\ell m }^{R_{AB}}\frac{\sin(kR_{AB})}{k^3 R_{AB}}-\sigma_{\ell p}F_{m p}^{\bar{R}_{AB}}\frac{\sin(k\bar{R}_{AB)})}{k^3\bar{R}_{AB}}\biggr]\frac{\sin^2(({\omega_k}-\omega_0)t/2)}{(({\omega_k}-\omega_0)/2)^2} ,
\end{eqnarray}

\begin{eqnarray}
\label{eq:23}
P^{(1)}({\omega_k},t)&=&
\frac{k^3 }{2\pi\hbar}
a\sigma_{\ell p}\biggl[\sum_{u=A}^B(\boldsymbol\mu_u^{eg})_{\ell}(\boldsymbol\mu_u^{eg})_{m} (\hat{\bf n}\cdot\nabla^{\bar{R}_u})F_{m p}^{\bar{R}_u}\frac{\sin(k\bar{R}_u)}{k^3\bar{R}_u}\pm 2(\boldsymbol\mu_A^{eg})_{\ell}(\boldsymbol\mu_B^{eg})_{m} (\hat{\bf n}\cdot\nabla^{\bar{R}_{AB}})F_{m p}^{\bar{R}_{AB}}\frac{\sin(k\bar{R}_{AB})}{k^3\bar{R}_{AB}}\biggr]\nonumber\\
&\ &\times h_1({\omega_k}-\omega_0,\omega_p,t) ,
\end{eqnarray}

\begin{eqnarray}
\label{eq:24}
P^{(2)}({\omega_k},t) &=& -\frac{k^3 }{2\pi\hbar}
\frac{a^2}{2}\sigma_{\ell p} \biggl[\sum_{u=A}^B(\boldsymbol\mu_u^{eg})_{\ell}(\boldsymbol\mu_u^{eg})_{m}(\hat{\bf n}\cdot\nabla^{\bar{R}_u})^2 F_{m p}^{\bar{R}_u}\frac{\sin(k\bar{R}_u)}{k^3\bar{R}_u}\pm2(\boldsymbol\mu_A^{eg})_{\ell}(\boldsymbol\mu_B^{eg})_{m}(\hat{\bf n}\cdot\nabla^{\bar{R}_{AB}})^2 F_{m p}^{\bar{R}_{AB}}\frac{\sin(k\bar{R}_{AB})}{k^3\bar{R}_{AB}}\biggr]\nonumber\\
&\ &\times \Big[ h_2({\omega_k}-\omega_0,\omega_p,t)+h_3({\omega_k}-\omega_0,\omega_p,t) \Big] .
\end{eqnarray}
\end{widetext}
Here
\begin{eqnarray}
\label{eq:25}
F_{\ell m}^{r}=(-\delta_{\ell m}\nabla^2+\nabla_{\ell}\nabla_m)^r
\end{eqnarray}
is a differential operator acting on variable $r$, $R_{AB}=\lvert{\mathbf r}_A-{\mathbf r}_B\rvert$,
$\bar{R}_{A(B)}=\lvert {\mathbf r}_{A(B)}-
\sigma{\mathbf r}_{A(B)}\rvert$, $\bar{R}_{AB}=\lvert {\mathbf r}_A-\sigma{\mathbf r}_B\rvert$, and ${\mathbf r}_A$, ${\mathbf r}_B$ respectively being the positions of atoms A and B.

A comparison of these expressions with the analogous quantity for the static-mirror case, shows that the main difference is the presence of terms related to the oscillation frequency of the mirror, specifically two new lateral peaks in the spectrum at frequencies ${\omega_k}=\omega_0\pm\omega_p$. Their relative intensities are of the order of $a/\bar{R}_i$ (see Eq.~\eqref{eq:23}), and $(a/\bar{R}_i)^2$ (see Eq.~\eqref{eq:24}), and give a qualitative change of the spectrum.
We wish to point out that secondary lateral peaks at frequency ${\omega_k}=\omega_0\pm2\omega_p$, stemming from second-order terms in the expansion in $a$, are also present (as Eq. \eqref{eq:19} shows). They represent, at the order considered, a sort of nonlinear effect; however, within the range of validity of our approximations, they give a quite small contribution to the overall spectrum.

Our expression for $P({\omega_k},t)$ is valid for a generic geometric configuration of the two atoms with respect to the oscillating plate.
\begin{figure}[h]
\includegraphics[width=8.0 cm]{fig2}
\caption{Spectrum (scaled with respect to the total emission probability) emitted by the two-atom system, prepared in the correlated symmetric state, as a function of the detuning ${\omega_k} -\omega_0$, both in the static case (green line) and in the dynamical case, with the two lateral peaks (red line). The atoms are aligned perpendicularly to the mirror, with dipole moments along the $x$-axis (parallel to the plate). The figure clearly shows that the presence of a dynamical mirror  produces two lateral peaks (red line) shifted from the central peak by the mirror's modulation frequency.  The inset shows a zoom of the central peak in the two cases considered. Parameters are chosen such that $a=2\times 10^{-7}\,$m, $z^0_A = 10^{-6}\,$m, $z^0_B= 1.1\times10^{-6}\,$m, $\omega_p =1.5\times10^{9}\,$s$^{-1}$, $\omega_0 = 10^{15}\,$s$^{-1}$, $t =1.6\times10^{-7}\,$s, $\mu\sim10^{-30}$C$\cdot$m.}
\label{fig:2a}
\end{figure}
\begin{figure}[h]
\includegraphics[width=8.0 cm]{fig3}
\caption{Spectrum (scaled with respect to the total emission probability) emitted by the two-atom system, prepared in the correlated symmetric state, as a function of the detuning ${\omega_k} -\omega_0$, both in the static case (green line) and in the dynamical case with the two lateral peaks (blue line). The dipole moments are perpendicular to the plate (along the $z$-axis). As before, the presence of a dynamical mirror  produces two lateral peaks (blue line) shifted from the central peak by the mirror's modulation frequency.  The inset shows a zoom of the central peak in the two cases considered (the two curves practically overlap each other) . The numerical values of the parameters are the same as in the plot in Fig. \ref{fig:2a}.}
\label{fig:2b}
\end{figure}
\begin{figure}[h]
\includegraphics[width=8.0 cm]{fig4}
\caption{Comparison between the emitted spectra (scaled with respect to the total emission probability) by the two-atom system, when the dipole moments are aligned parallel (red line) and perpendicular (blue line) to the plate. The figure shows that the lateral peaks in the emitted spectrum by dipole moments aligned along the $z$-axis are smaller than those obtained in the case of dipole moments oriented parallel to the mirror (along the $x$-axis). The inset shows a zoom of the central peak in the two cases considered. The numerical values of the parameters are the same as in Fig. \ref{fig:2a}.}
\label{fig:2c}
\end{figure}

In order to get a clear physical insight it is helpful to analyze $P({\omega_k},t)$ in the specific case of atoms aligned along the $z$ axis (i.e. perpendicularly to the mirror), for example when ${\mathbf r}_A=(0,0,z^0_{A})$ and ${\mathbf r}_B=(0,0,z^0_{B})$.
Figure \ref{fig:2a} shows the spectrum (scaled with respect to the total emission probability) in the symmetric case and in the limit of long times, as a function of the detuning ${\omega_k} -\omega_0$: the red line shows the dynamical case, while the green line shows the static-mirror case. As the figure shows,
the presence of the dynamical mirror determines the two symmetric lateral peaks shifted from the central peak by the modulation frequency. These two lateral peaks are symmetric with respect to the central peak, because the photonic density of states is essentially the same at the two frequencies. Analogous lateral peaks were found for a single two-level atom located near an oscillating mirror~\cite{ferreri}. A similar result is obtained for dipole moments aligned perpendicularly to the mirror, as figure \ref{fig:2b} shows. Interestingly, although the image dipole of $\boldsymbol\mu_{\perp}$ is
still $\boldsymbol\mu_{\perp}$, and a constructive interference between the atomic dipoles and their mirror images is expected, the intensity of the two lateral peaks in the emitted spectrum is smaller than that obtained in the case of dipole moments oriented parallel to the plate, as shown in figure \ref{fig:2c}. This effect seems to suggest that the oscillation of the mirror can induce a sort of destructive interference between the atomic dipoles and their images, oriented along the $z$-direction, parallel to the motion of the plate.

We have also considered the emitted spectrum by the two-atom system at different times. The results obtained are illustrated in Fig. \ref{fig:2d}, for two atoms prepared in a symmetric superposition with dipole moments  oriented parallel to the oscillating mirror.  The figure shows that  the central and the lateral peaks increase with time, as expected.
\begin{figure}[!hbpt]
\includegraphics[width=8.0 cm]{fig5}
\caption{Comparison between the emitted spectra (scaled with respect to the total emission probability) by the two-atom system, at different times. The dipole moments are aligned parallel to the plate. Continuous green line, blue line, and red line refer to the emitted spectrum at times $t=10^{-8}$s (continuous green), $t=3\times 10^{-8}$s (continuous blue), $t=6\times 10^{-8}$s (continuous red), respectively. The figure shows that the central peak (see inset on the left) and the two lateral peaks (see inset on the right) in the spectrum increase with time, as expected. The numerical values of the other parameters are the same as in Fig. \ref{fig:2a}.}
\label{fig:2d}
\end{figure}

Finally, we wish to stress that our results are in principle detectable using current experimental techniques; for example, for two hydrogen atoms and typical optical transitions, the natural linewidth is of the order of $ \sim 10^8 \,$s$^{-1}$; thus an oscillation frequency in the range $\omega_p \sim 10^9 - 10^{10} \,$s$^{-1}$, that can be currently obtained exploiting the technique of dynamical mirrors~\cite{braggio1,antezza}, is sufficient to resolve the lateral lines in the emitted spectrum.

\section{\label{sec:3}Collective spontaneous decay rate of the two-atom system}
We now evaluate the decay rate of the two-atom system to the ground state. This is obtained by integrating $P({\omega_k},t)$ over $k$, and then taking its time derivative,

\begin{eqnarray}
\label{eq:30}
&\ &\Gamma(t)= \frac{d}{d t}\int_{0}^{\infty} d\omega_k P({\omega_k},t) .
\end{eqnarray}
Since the functions $h_0(\omega_k-\omega_0,t)$ and $h_i(\omega_k-\omega_0,\omega_p,t)$ ($i=1,2,3$) are strongly peaked at $\omega_k\sim\omega_0$ and $\omega_k\sim\omega_0\pm\omega_p$, we can approximate the space-dependent functions in \eqref{eq:22}-\eqref{eq:24}, by their expressions in $k_0$ (taking also into account that $\omega_p\ll ck_0$) and then take them out of the integrals.
Taking into account only terms up to the first order in the expansion \eqref{eq:12} on the mirror's oscillation amplitude, a straightforward calculation gives
\begin{eqnarray}
\label{eq:31}
\Gamma(t)=\Gamma_A(t)+\Gamma_B(t)\pm\Gamma_{AB}(t) ,
\end{eqnarray}
where
\begin{widetext}
\begin{eqnarray}
\label{eq:32}
\Gamma_{A(B)}(t)=\frac{k_0^3}{\hbar}(\boldsymbol\mu_{A(B)}^{eg})_{\ell}(\boldsymbol\mu_{A(B)}^{eg})_{m}\biggl[\frac 2 3 \delta_{\ell m}-\sigma_{\ell p}F_{m p}^{\bar{R}_{A(B)}}\frac{\sin(k_0\bar{R}_{A(B)})}{k_0^3\bar{R}_{A(B)}}+2a\sin(\omega_p t)\sigma_{\ell p}(\hat{\bf n}\cdot\nabla^{\bar{R}_{A(B)}}) F_{m p}^{\bar{R}_{A(B)}}\frac{\sin(k_0\bar{R}_{A(B)})}{k_0^3\bar{R}_{A(B)}}\biggr] ,
\end{eqnarray}
\begin{eqnarray}
\label{eq:33}
\Gamma_{AB}(t)=\frac{2k_0^3}{\hbar}(\boldsymbol\mu_{A}^{eg})_{\ell}(\boldsymbol\mu_{B}^{eg})_{m}\biggl[F_{\ell m }^{R_{AB}}\frac{\sin(k_0R_{AB})}{k_0^3R_{AB}}-\sigma_{\ell p}F_{m p}^{\bar{R}_{AB}}\frac{\sin(k_0\bar{R}_{AB})}{k_0^3\bar{R}_{AB}}+2a\sin(\omega_p t)\sigma_{\ell p}(\hat{\bf n}\cdot\nabla^{\bar{R}_{AB}}) F_{m p}^{\bar{R}_{AB}}\frac{\sin(k_0\bar{R}_{AB})}{k_0^3\bar{R}_{AB}}\biggr] \, .
\end{eqnarray}
\end{widetext}

The expressions \eqref{eq:31}-\eqref{eq:33} are general, valid for a generic configuration of the two atoms with respect to the plate, and show oscillations of the decay rate with time, directly related to the adiabatic motion of the mirror. In fact, the emission rate of our system shows a term that oscillates in time by following the mirror's law of motion, of course. This is strictly related to our hypothesis of adiabatic motion of the boundary.
In order to discuss in more detail this result, similarly to what we did in the previous section, we analyze the specific case of atoms aligned along the $z$-direction, i.e. perpendicular to the reflecting plate. In this case of a perpendicular orientation we obtain
\begin{widetext}
\begin{eqnarray}
\label{eq:34}
&\ &\Gamma_{A}(t) = \frac{k_0^3}{\hbar}(\boldsymbol\mu_{A}^{eg})_{\ell}(\boldsymbol\mu_{A}^{eg})_{m}\biggl\{\frac 2 3 \delta_{\ell m}-\sigma_{\ell p}\biggl[-\left(\delta_{p m}-3({\hat{\bar{R}}_{A}})_{p}({\hat{\bar{R}}_{A}})_{m}\right)\left(\frac{\sin{k_0\bar{R}_{A}}}{k_0^3\bar{R}_{A}^3}-\frac{\cos{k_0\bar{R}_{A}}}{k_0^2\bar{R}_{A}^2}\right)\nonumber\\
&\ &+\left(\delta_{p m}-({\hat{\bar{R}}_{A}})_{p}({\hat{\bar{R}}_{A}})_{m}\right)\frac{\sin{k_0\bar{R}_{A}}}{k_0\bar{R}_{A}}\biggr]+\frac{2a\sin(\omega_p t)}{\bar{R}_{A}}\sigma_{\ell p}\biggl[\left(\delta_{p m}-({\hat{\bar{R}}_{A}})_{p}({\hat{\bar{R}}_{A}})_{m}\right) \cos{k_0\bar{R}_{A}}\nonumber\\
&\ & -2\left(\delta_{p m}-3({\hat{\bar{R}}_{A}})_{p}({\hat{\bar{R}}_{A}})_{m}\right)\frac{\sin k_0\bar{R}_{A}}{k_0\bar{R}_{A}}+3\left(\delta_{p m}-5({\hat{\bar{R}}_{A}})_{p}({\hat{\bar{R}}_{A}})_{m}\right)\left(\frac{\sin{k_0\bar{R}_{A}}}{k_0^3\bar{R}_{A}^3}-\frac{\cos{k_0\bar{R}_{A}}}{k_0^2\bar{R}_{A}^2}\right)\nonumber\\
&\ &-\left(\delta_{mz}{(\hat{\bar{R}}_{A}})_{p}+\delta_{pz}{(\hat{\bar{R}}_{A}})_{m}\right)\left(\frac{\sin{k_0\bar{R}_{A}}}{k_0\bar{R}_{A}}
+3\frac{\cos{k_0\bar{R}_{A}}}{k_0^2\bar{R}_{A}^2}-3\frac{\sin{k_0\bar{R}_{A}}}{k_0^3\bar{R}_{A}^3}\right)\biggr]\biggr\} ,
\end{eqnarray}
\end{widetext}
\begin{eqnarray}
\label{eq:35}
&\ &\Gamma_B(t)=(\Gamma_A(t) \,\,\, \text{with}\, A \rightarrow B) ,
\end{eqnarray}
\begin{widetext}
\begin{eqnarray}
\label{eq:36}
&\ &\Gamma_{AB}(t) = \frac{2k_0^3}{\hbar}(\boldsymbol\mu_{A}^{eg})_{\ell}(\boldsymbol\mu_{B}^{eg})_{m}\biggl\{\biggl[-\left(\delta_{\ell m}-3({\hat{R}_{AB}})_{\ell}({\hat{R}_{AB}})_{m}\right)\left(\frac{\sin{k_0 R_{AB}}}{k_0^3 R_{AB}^3}-\frac{\cos{k_0 R_{AB}}}{k_0^2 R_{AB}^2}\right)\nonumber\\
&\ &+\left(\delta_{\ell m}-({\hat{R}_{AB}})_{\ell}({\hat{R}_{AB}})_{m}\right)\frac{\sin{k_0 R_{AB}}}{k_0 R_{AB}}\biggr]+\sigma_{\ell p}\biggl[\left(\delta_{p m}-3({\hat{\bar{R}}_{AB}})_{p}({\hat{\bar{R}}_{AB}})_{m}\right)\left(\frac{\sin{k_0\bar{R}_{AB}}}{k_0^3\bar{R}_{AB}^3}-\frac{\cos{k_0\bar{R}_{AB}}}{k_0^2\bar{R}_{AB}^2}\right)\nonumber\\
&\ &-\left(\delta_{p m}-({\hat{\bar{R}}_{A}})_{p}({\hat{\bar{R}}_{AB}})_{m}\right)\frac{\sin{k_0\bar{R}_{AB}}}{k_0\bar{R}_{AB}}\biggr]+\frac{2a\sin(\omega_p t)}{\bar{R}_{AB}}\sigma_{\ell p}\biggl[\left(\delta_{p m}-({\hat{\bar{R}}_{AB}})_{p}({\hat{\bar{R}}_{AB}})_{m}\right) \cos{k_0\bar{R}_{AB}}\nonumber\\
&\ & -2\left(\delta_{p m}-3({\hat{\bar{R}}_{AB}})_{p}({\hat{\bar{R}}_{AB}})_{m}\right)\frac{\sin k_0\bar{R}_{AB}}{k_0\bar{R}_{AB}}+3\left(\delta_{p m}-5({\hat{\bar{R}}_{AB}})_{p}({\hat{\bar{R}}_{AB}})_{m}\right)\left(\frac{\sin{k_0\bar{R}_{AB}}}{k_0^3\bar{R}_{AB}^3}-\frac{\cos{k_0\bar{R}_{AB}}}{k_0^2\bar{R}_{AB}^2}\right)\nonumber\\
&\ &-\left(\delta_{mz}{(\hat{\bar{R}}_{AB}})_{p}+\delta_{pz}{(\hat{\bar{R}}_{AB}})_{m}\right)\left(\frac{\sin{k_0\bar{R}_{AB}}}{k_0\bar{R}_{AB}}
+3\frac{\cos{k_0\bar{R}_{AB}}}{k_0^2\bar{R}_{AB}^2}-3\frac{\sin{k_0\bar{R}_{AB}}}{k_0^3\bar{R}_{AB}^3}\right)\biggr]\biggr\} .
\end{eqnarray}
\end{widetext}

Expressions (\ref{eq:34}-\ref{eq:36}) show that the motion of the mirror yields new time-dependent terms of the order of $a/\bar{R}_{A/B}$ and $a/\bar{R}_{AB}$. We have neglected second-order terms in the perturbative expansion; this approximation is valid for small oscillation amplitudes with respect to other relevant length scales in the system, that is for $a\ll \bar{R}_{A/B},\bar{R}_{AB}$ and $a\ll k_0^{-1}$. For example, for $k_0 \sim 10^7 \,$m$^{-1}$, $R_{A/B} \sim 10^{-6} \,$m, and $a=10^{-8} \,$m, we have $a/\bar{R}_{A/B}, \, a/\bar{R}_{AB} \sim 10^{-1}$, \, $k_0 a \sim 10^{-1}$, and we neglect the second-order term proportional to $a^2$. The conditions above are within reach of currently achievable experimental techniques.
\begin{figure}
\includegraphics[width=8.0 cm]{fig6a}
\caption{Plot of the collective decay rate for two atoms prepared in the correlated symmetric state, at different times, as a function of the distance of atom $B$ from the mirror, when the atom $A$ is kept fixed ($R_A=z_A=1.25\times 10^{-6}$m). The atoms are aligned along the $z$ direction, with dipole moments parallel to the mirror. Continuous red line, blue dashed line, orange dotted line refer to two atoms near the oscillating mirror, at times $t=2\times 10^{-7}$s (continuous red), $t=2.3\times 10^{-7}$s (blue dashed), $t=2.4\times 10^{-7}$s (orange dotted), respectively. Dot-dashed green line refers to two atoms in the presence of a static mirror.
We have also used $a=2\times 10^{-7}\,$m, $\omega_p =1.5\times10^{9}\,$s$^{-1}$, $\omega_0 = 10^{15}\,$s$^{-1}$.}
\label{fig3}
\end{figure}
\begin{figure}
\includegraphics[width=8.0 cm]{fig7a}
\caption{Plot of the collective decay rate for two atoms prepared in the correlated antisymmetric state, at different times, as a function of the distance of atom $B$ from the mirror, when the atom $A$ is kept fixed ($R_A=z_A=1.25\times 10^{-6}$m). The atoms are aligned along the $z$ direction, with dipole moments parallel to the mirror, Continuous red line, blue dashed line, orange dotted line refer to two atoms near the oscillating mirror, at times $t=2\times 10^{-7}$s (continuous red), $t=2.3\times 10^{-7}$s (blue dashed), $t=2.4\times 10^{-7}$s (orange dotted), respectively. The green dot-dashed line refers to two atoms near a static mirror.
The other relevant parameters are the same of Fig. \ref{fig3}.}
\label{fig4}
\end{figure}

Figure \ref{fig3} shows the scaled (with respect to Einstein coefficient $A$, given in (\ref{eq:1})) collective decay rate at different times, as a function of the distance of atom $B$ from the mirror's average position, when atom $A$ is at a fixed position. The two atoms are aligned orthogonal to the mirror and prepared in the symmetric state. The dipole moments are parallel to the mirror. The figure shows that the decay rate oscillates in time, and that, at a given time, in specific distance ranges it can be increased (in the figure, see the red continuous line, blue dashed line and orange dotted line) with respect to the static-mirror case (green dot-dashed line); in other distance ranges, the opposite occurs. Analogous results are obtained in the case of atoms prepared in an antisymmetric configuration, as shown in figure \ref{fig4}.

In conclusion, our results show that the spectrum of the emitted radiation can be qualitatively changed exploiting the oscillation of the plate, and that the collective spontaneous emission can be controlled (enhanced or suppressed) by modulating in time the position of the mirror. This suggest the possibility to control also other radiative processes by modulated (time-dependent) environments, for example the resonance energy transfer between atoms or molecules.

\section{\label{sec:4}Conclusion}
In this paper, we have discussed the collective spontaneous decay of a system of two identical two-level atoms prepared in a correlated (symmetric or antisymmetric) {\em Bell-type} state, and located near an oscillating perfectly reflecting plate, in the adiabatic regime.
We have first discussed in detail the effect of the motion of the mirror on the spectrum of the radiation emitted by the two atoms, and then their collective spontaneous decay rate. We have shown that the motion of the mirror strongly affects the features of the spectrum, which exhibits, in addition to the usual peak at $\omega=\omega_0$, two new lateral peaks separated from the atomic transition frequency by the oscillation frequency of the plate, similarly to previous results for the single-atom decay~\cite{ferreri}.
We have also found that the decay rate to the collective ground-state is modulated in time, and can be increased or decreased, compared with the static-boundary case, according to time and atoms-wall distances, by exploiting the oscillating boundary. Our results show that modulated environments can give additional possibilities, with respect to fixed boundaries, to manipulate and tailor atomic radiative processes such as the cooperative spontaneous emission; also, they strongly indicate a similar possibility for other relevant radiative processes such as the energy transfer between two atoms, or the resonance interaction energy between correlated atoms. We will consider these physical systems in a future publication.

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