In March of 2016, the Lincoln Navigator Concept was unveiled to the world at the New York International Car Show. It was a taste of what was to come, minus the gullwing doors and Cinderella steps, mind you. The concept introduced an attractive set of "turbine-style" rims, fancier fascia, and sleek design that was retained for the newest rendition of the Navigator, the 2018 model year. It has been a long time coming.
The last time we got to see a newly designed Lincoln Navigator, former President George W. Bush was still in the White House. After a decade with the last generation of Navigator, Ford has finally given us the newly designed 2018 Lincoln Navigator. Lincoln's heaviest production vehicle gets 200 lbs lighter with a new aluminum body. It retains a body-on-frame construction, sharing the T3 platform with the Ford Expedition and Ford F-Series, and title of traditional SUV.
The abrupt nose squares off the fascia, adorned with a chrome, mesh-filled rectangular grille. The Lincoln logo sits in the center, reminiscent of the appearance of 2017 Lincoln Continental and MKZ grilles. Hood creases jut up and out from either side of the grille, and the headlights sweep back around the corners. LED running lights and new intake design gives the 2018 Navigator a stauncher appearance. The chrome beltline moves around the rear of the vehicle, where the east to west taillights sit below chrome LINCOLN badging. A subtle rear spoiler sits atop of the liftgate.
When approaching, take note of some of the intimate details: chrome trim, running boards, black tinted pillars that blend into the rear windows, and a light show. Yes, a light show. The Navigator features a series of greeting lights as the owner approaches, including an illuminated grille badge, running lights, "welcome mat" below the front doors that projects the Lincoln logo, illuminated door handles, interior lights, and even seatbelts as you enter.
An all-new interior design features quality, soft touch materials and a luxurious design and technology upgrades that match Lincoln's Continental. Sound proofing has been augmented, offering a quieter drive. Hop in the 30-way power adjustable seats, designed for maximum comfort, and you won't mind long commutes cross-country with the family. In fact, the passenger-side front seat offers the same 30-way functionality, including massage, heating, and cooling functionality. The rear seats are extremely comfortable as well, as the roomy Navigator allows for ample, best-in-class legroom and optional captain's chairs in the second row and reclining third-row seats.
Passengers can enjoy an available rear-seat entertainment system with a 10-inch adjustable screen. Content can be accessed through an SD card, HDMI, USB, SYNC AppLink, or even Sling Media, allowing for owners of a Slingbox to access their TV channels. Standard Wi-Fi allows for up to 10 mobile devices to be connected at once. To add to the connectivity and technology plethora, Ford's SYNC 3 infotainment system comes standard, integrating Apple CarPlay and Android Auto. Audio is played through a 20-speaker system.
Occupants can keep devices charged in one of several ways, including six USB ports, four 12-volt power outlets, an 110-volt plug, and an available wireless phone charger in the first-row center console. An intuitive 12-inch instrument cluster with available integrated Head-Up display allows drivers to better keep their eyes on the road and at the ready.
As to storage, one of the biggest advantages of the Navigator (pardon the pun, it was intended), there are several areas to store items, both large and small, including 17 cup holders. An adjustable shelf sits behind the third row with a lip that keeps your items from rolling out of the back when the door is open, second and third-row seats fold down for an immense amount of capacity, and a foot activated tail lift sensor sits beneath the bumper.
Check out our Top 10 Full-Size Cargo SUVs.
The Navigator features a revised twin turbocharged 3.5L V6 engine, paired with a new 10-speed automatic transmission and auto start/stop technology. Horsepower has been increased by 70 HP over the previous generation, now at 450 HP. Torque has also been increased by 40 lb-ft, coming in at 500 lb-ft of torque. Both rear-wheel and all-wheel drive are available. It's a great combination of speed and power to kick up some wind through the turbine rims as the Navigator blows past.
While towing capacity numbers haven't been released yet, given the engine output and corporate cousin's anticipated numbers, the Navigator should be in the 9,000 lb. plus club while in towing mode. Towing mode is activated automatically by the onboard computer when a trailer is attached. The 12-inch digital dash cluster allows for other modes, including Eco (Conserve), Sport (Excite), Slippery (rain and ice), Deep (snow and mud), and Slow Climb (steep hills).
The 2018 Lincoln Navigator safety features and crash test ratings have not been disclosed yet. However, some available features include a 360-degree camera and enhanced park assist system, integrating views from four cameras for an overhead view of the entire vehicle. Trailer Backup Assist will also be available, as will adaptive cruise control. Speed-dependent adaptive lighting is a new Lincoln technology that debuts with the Navigator and provides a wider spread of light at lower speeds for driving in residential areas at night.
The 2018 Lincoln Black Label Navigator offers privileges that include extended premium services, anytime car washes, annual detailing, and exclusive memberships to select restaurants and Avis President's Club. Three designer themes are available for the interior – Yacht Club, Destination, and Chalet.
Lincoln placed a starting price tag of $72,055 on the 2018 Navigator, a jump from the starting price of the 2017 (of around $64,000), but still below that of the Cadillac Escalade. With production underway and an anticipated roll out for fall of 2017, we really can't be more excited to see a finished product. A fully connected luxurious people mover with power and grace – we couldn't have asked for much more. We'll keep you updated as details continue to unfold on this exciting full-size SUV.


Begin by entering the Sound Test code - however, press Right, not Down, at the end of the cheat. Time will increase much, much faster.
At the title screen, on controller 2, hold A and keep holding. Hold B, then release B, then hold B again. Release A, then hold A again. Release B, then hold B again. Release A, then hold Right. Finally, release both Right and B. Now you can press the directional pad on controller 2 to hear the music or sound effects.


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Home News Film 'Beatriz at Dinner' is a small film that packs an earth-shattering punch
'Beatriz at Dinner' is a small film that packs an earth-shattering punch
Leigh Monson
There are films that make their stamp by their mere existence. As much as film writers love to explore the specifics of technical specifics such as quality of editing, dynamic cinematography, or special effects, sometimes all that's necessary for a film to achieve greatness is a good set, a great cast of actors, and a hell of a script, assuming the scale of the story the film is telling is appropriate for that modest attempt. Beatriz at Dinner is just one of these small scale productions, but its aspirations are anything but modest, as it showcases some of the best performances we're likely to see all year in a story that is at once intimately personal and earth-shatteringly universal in its relevance.
Beatriz (Salma Hayek) is a holistic healer who works part-time as masseuse in order to make ends meet. One day as she is massaging a wealthy client (Connie Britton), her car breaks down, stranding her as this client and her husband (David Warshofsky) prepare for a dinner party with some business associates. Beatriz stays for dinner, interacting with the wealthy echelons of American business and coming to realize the terrible reality of who she is spending time with.
Hayek delivers the performance of a career as a Mexican immigrant with not much in the way of traditional schooling, but is very intelligent with a passion for healing and preserving the world against the capitalistic forces that do damage to the environment and the impoverished. These are in turn personified by dinner guest Doug Strutt (John Lithgow), a real estate mogul who leads a cackling crew of tone deaf sycophants (played perfectly to type by Chloë Sevigny, Amy Landecker, and Jay Duplass) in a torrent of microaggressions, dismissals, and interruptions that betray attitudes of cultural and racial supremacy as they celebrate further wealth at the misfortune of others. What results is a drama of manners in which Beatriz is constantly torn between being a polite guest and standing up for what she believes in as she is ridiculed by smiling faces that expect her to take it in stride, and the tension is palpable and fragile enough to be cut with a butter knife. Director Miguel Arteta and cinematographer Wyatt Garfield do an excellent job of framing Beatriz as a woman apart from her captors, held in a cage of niceties that pushing against would cause the entire party to turn against her.
What elevates Beatriz at Dinner into the realm of brilliance, though, is in how the villains of this piece don't see themselves as such, but are quick to dismiss any confrontation of their cloistered worldview as simply Beatriz's emotions running high, or that they do minor good for the world along with their willfully ignorant evil, or that they have only good intentions and that they only want to live life to the fullest. These are characters unfamiliar with listening to perspectives different from their own, but they are so comfortable in their ignorance that they refuse to even attempt an understanding of why Beatriz might be upset with them. It's a brutal examination of American classism that highlights precisely why the wealthy lack the necessary empathy to counteract the harm they do to the world.
Alternately fatalistic and hopeful, Beatriz at Dinner is a roller coaster of emotional payoff, taking a small and modest offering and exploding what one's expectations might be for a film about people sitting around a dinner table talking. It's not a flashy film because it doesn't need to be; much like its protagonist, it shows up, makes a point, and, while acknowledging that the encounter won't bring about any immediate change, plants a seed of hope that the struggle is at least somewhat worthwhile. This is a film that will blow you away if you give it a chance to say its piece, and listening is the very least any of us can do.
Beatriz at Dinner
Alternately fatalistic and hopeful, Beatriz at Dinner is a roller coaster of emotional payoff, taking a small and modest offering and exploding what one's expectations might be for a film about people sitting around a dinner table talking.
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Leigh Monson is technically a licensed attorney but somehow thinks being Substream's Film Editor is a lot more fun. Leigh loves both award darlings and hilariously bad films, does not believe in superhero movie fatigue, and calls it like they see it.

redpajama_set_name: RedPajamaCommonCrawl


This unit is being remodeled and will be delivered end of November modern, clean and ready to move in!
301 Jefferson Ave Apt 3A is located in South Point neighborhood in the city of Miami Beach, FL.
Checkout other home values in Jefferson Ave.
Homes near 301 Jefferson Ave Apt 3A have a median list price of $259,000 and a median price per square foot of $390.
301 Jefferson Ave Apt 3 A, Miami Beach, FL 33139 is a condo/townhome/row home/co-op for sale listed on the market for 188 days. 301 Jefferson Ave Apt 3 A is in the South Point neighborhood, which has a median listing price of $1,050,000. The median listing price for South Point is 102% greater than Miami Beach at $518,700, and 105% greater than FL at $513,000. Nearby neighborhoods like South Beach, SoFi, Ocean Front and Bayshore have a median listing price of $750,000. There are similar and nearby condo/townhome/row home/co-ops for sale at 301 Jefferson Ave Apt 6 B, 344 Meridian Ave Apt 3 B and 631 Jefferson Ave Apt 205.


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Slight increase in number of applications to art and design courses
Applications to UK creative arts and design courses starting in September are marginally up on last year, according to new figures.
By Angus Montgomery January 31, 2013 11:23 am February 18, 2015 8:52 am
Source: Simononly
The University and Colleges Admissions Service says there has been a 2.4 per cent year-on-year increase in applications.
However, this follows a 16.3 per cent drop in the number of applications measured at this time last year.
The 2.4 per cent increase is also slightly lower than the 3.5 per cent increase in applications to all subjects.
Last year's dip in application numbers followed changes to the higher-education system, which saw university fees for some undergraduate courses rise to £9000.
Ucas has suggested this the boost to this year's figures may have come from 19-year-olds who put off applying to university last year, when the fees were increased.
However, it also says the new figures show that applications from 'disadvantaged' 18-year-olds are close to record levels, in spite of the increase in fees.
Mary Curnock Cook, chief executive of Ucas, says, 'This is an encouraging report, with no double-dip for applications and continuing improvements for disadvantaged groups.
'The significant increase in 19-year-olds applying may be indicating that some young people delayed their decisions about higher education after leaving school last year.'
January 2013 Projects
Passnotes – Design and the English Baccalaureate
Rose creates V&A Schools designs
A new identity for Olympia
Four Corners – an interview with Chuck Harrison
Brandimage's slanted identity for low-cost airline HOP!
What was your first formative project?


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Have you had a soul exchange? Do you feel strange as if you are a different person in the same body? Have you had a rapid shift in lifestyle? You may be a walk-in soul who is here as a starseed from another dimension. Figuring out how to anchor your expanded consciousness in the physical human body may be a challenge for you.
This website and Yvonne Perry's book for walk-ins, Walk-ins Among Us ~ Open Your Personal Portal to Cosmic Awareness shares the ways a walk-in can occur and some indications that a soul exchange has happened.
There are several different types of walk-ins. Some exchanges are between two unrelated souls (differing soul groups, monads, or oversouls) who have partnered for a particular (or multiple) incarnation. Other walk-ins involve primary soul mates from a group of souls (matrix) governed by the same monad, the perfect God essence or consciousness. Much like the brain is to the body, a monad is the highly-developed nucleus of a system. The monad is the ultimate guidance or control center of a group of souls that includes twin flames, soul mates, and soul aspects such as personalities and archetypes: inner child, the critical parent, the wounded healer, etc. A monad supplies the life-force, love, and attention needed to maintain an embodied soul's existence on Earth as well as in non-physical realms. Your personal monad is responsible for your evolution as it ensures that all aspects of your being work in harmony toward soul integration. In spiritual terms, one monad contains twelve oversouls and each oversoul has twelve personalities (144 soul aspects). Learn more about walk-ins and soul exchanges.
Some bodies hold space on the Earth plane for many souls in a group to pass through over a lifetime. These "revolving door" walk-ins are like an inn where a soul or soul aspect may stay for a short while and then move on when the mission is complete. You will meet some of them in Walk-ins Among Us.
There are many variations of walk-ins and soul exchanges, so do not get caught up in labeling your experience. Each one is unique, depending upon the life situation of the natal soul, the background of the incoming spirit, and Earth's evolutionary condition at the time of the walk-in. If you are a walk-in, use this book as a reference to understand your own experience.
Yvonne is available as a coach for walk-ins and starseeds who are here to help humanity ascend.


I want to tell you a story. Everyone likes a story, right? But at the heart of my story lies a confession that I am afraid will shock many readers.
People assume that because I teach math, blog about math, give advice about math on internet forums, and present workshops about teaching math — because I do all this, I must be good at math.
Apply logic to that statement.
The conclusion simply isn't valid.
Photo by Eirik Newth via flickr.
In a lazy, I-don't-want-to-do-school mood, Princess Kitten was ready to stop after three math problems. We had gotten two of them correct, but the last one was counting the ways to paint a cube in black and white, and we forgot to count the solid-color options.
For my perfectionist daughter, one mistake was excuse enough to quit. She leaned her head against me as we sat together on the couch and said, "We're done. Done, done, done." If she could, she would have started purring — one of the most manipulative noises known to humankind. I'm a soft touch. Who can work on math when there's a kitten to cuddle?
Photo by George Parrilla via flickr.
So we pulled out the Counting lessons in Competition Math for Middle School. [Highly recommended book!] Kitten doesn't like to compete, but she enjoys learning new ideas, and Batterson's book gives her plenty of those, well organized and clearly explained.
Pizzas at Mario's come in three sizes, and you have your choice of 10 toppings to add to the pizza. You may order a pizza with any number of toppings (up to 10), including zero. How many choices of pizza are there at Mario's?
Quilt: What Can You Do with This?
I know other teachers have done math quilts, but I've never gotten around to trying it in any of my classes. Still, this image caught my eye and practically begged me to make it into a math lesson for my elementary math club.
How could you use this image as a springboard to doing math? What questions would you ask? What concepts would you try to get across? What would you follow it with? Please comment!
Continue reading Quilt: What Can You Do with This?


Melissa of The Inspired Room (www.theinspiredroom.net) started a great discussion about using picture rails in a home. They allow great flexibility because you can move paintings, prints, photos and decorative plates into any room along the rails with picture rail hooks. No nails or holes required.
In our Australian 'Californian Bungalow' the picture rails are positioned 2/3 up the walls and are very popular in older-style homes.
In the first two pics, you can see that the walls are painted white above the picture rail and buttercup yellow below. It really brightens and opens up the room.
Our picture rails had originally been stained a dark brown, but we stripped them back to their natural timber. The third photo shows the solid red walls in our dining room.
In case you want to know the artist for each print.... The first photo at the top is a print by Lesa Delisi called 'Point of Interest'. The second is by Carolyn Blish. The third is Catherine Simpson's 'Homemade Soup'.
Back to the January Photo A Day Challenge!
Day 10 "Childhood" - there's nothing better than Star Wars Lego.
The photo frames above can be used for Day 9 "Routine" - if not the daily routine of cleaning them (which I certainly don't do enough of), then at least the routine of looking at them with enjoyment.
Day 8 "Sky" - over the Goulburn River in front of our house.
Day 7 "Favourite" dam on our farm where we can fish and boat.
New home needed for AGA stove!


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Prince Charles Talks Sustainable Fashion In New Interview
He feels it's the way to go!
Prince Charles Talks Importance Of Sustainable Fashion In New Interview: "There Are Huge Opportunities"
Prince Charles Talks Importance Of Sustainable Fashion In New Interview
(© Getty Images)
November 5, 2020 - 01:57 / Hayley Paskevich
In a new interview, Prince Charles discussed his lifelong interest in sustainable fashion! Charles talked about how he's managed to have many of his own pieces fixed up, and shared how conscious consumerism can help change the fashion industry. Find out what he said here!
Prince Charles has talked about the value of sustainable fashion in a brand-new interview! As People mentions, the December issue of British Vogue sees the royal opening up about how his eco-friendly approach to fashion has influenced his life for years, and sharing why sustainability is important to the future of the industry.
Charles comments on being considered a fashion icon
Prince Charles told British Vogue's editor-in-chief Edward Enninful that he appreciates the compliments he receives when it comes to his own personal fashion style! "I thought I was like a stopped clock – I'm right twice every 24 hours," Charles said of his sartorial choices. "But . . . I'm very glad you think it has style."
As British Vogue mentions, the royal then went on to talk about how he's able to get good use out of the pieces he cherishes, such as old suits and leather shoes. "I'm lucky because I can find marvellous people who are brilliant makers of the things that I appreciate," Charles explained, "and because of that, I try to keep them going for longer."
(© Chris J Ratcliffe - WPA Pool)
Charles talks potential opportunities through sustainability
Charles shared that his interest in sustainable fashion started at a young age, telling Enninful that he "would watch with fascination" while he saw shoes get repaired. "I happen to be one of those people who'd get shoes – or any item of clothing – repaired if I can, rather than just throw it away," he said.
"And that's why I think, from an economic point of view, there are huge opportunities for people to set up small businesses involved with repair, maintenance and reuse." As British Vogue mentions, Charles' Prince's Foundation currently has a special program for students underway that will result in a sustainable fashion collection, called The Modern Artisan Project.
Youth will need "vast" amounts of help!
Prince Charles Warns: "Uniquely Challenging" Times For The Youth
Charles says that consumers have "immense power"
Charles talked about why it's so crucial that young people in the fashion industry are given the opportunity to get immersed within the world of sustainable fashion. "The British fashion textile sector is of enormous importance," he explained. "But the trouble is, it requires constant investment in young people and in the development of real skills."
"And a lot of the students we train here are snapped up by local firms – the ones that are left in the textile sector," Charles continued. "But it seems to me there are huge opportunities, particularly now, within the whole sustainable fashion sector, to counter this extraordinary trend of throw-away clothing – or throw away everything, frankly."
Prince Charles, Prince of Wales visits the Defence Medical Rehabilitation Centre Stanford Hall in Loughborough, United Kingdom, 2020
Charles also shared what he believes is the most effective way to combat the fast fashion industry! "The consumer has immense power in deciding where to buy from," he explained, "and the best companies will lead the way, we hope, in demonstrating that if you follow the right principles of operation, not only are you moving more and more towards net-zero but also you're removing pollution from supply chains."
Earlier this year, Charles teamed up with designers for an eco-friendly fashion line. The royal has also spoken out on ecological issues, demanding "immediate action" when it comes to climate change!
"The sheer dishonesty of what I've seen..."
Charles Spencer Demands Inquiry Into BBC For Tricking Him and Sister Princess Diana
The Prince of Wales: Through The Years With Prince Charles
With her designer friend!
Duchess Meghan To Launch Fashion Line For Smart Works


To speak to a legal expert about changing your name today, call 01271 343457.
Changing your name, whether it be your first, middle, surname, or your entire name, can be done by way of a Change of Name Deed or other official document.
People change their names for a variety of reasons, such changing their surname back to their maiden name after divorce, to double barrell their name after marriage, to fit in with a new family such as a step family or simply because they have been known by another name for a period of time.
A change of name can be done at any time of your life provided it is not being done for fraudulent purposes, but if you want it recognised on official documents such as your passport, driving licence, bank accounts, and medical records, you will need to complete a Change of Name deed or other official document for it to be recognised by these official organisations.
In the UK, in order to change a child's name, everyone with parental responsibility must consent to the name change.
Under English law an unmarried father automatically acquires parental responsibility if he is named on the birth certificate from 1 December 2003.
It is also possible to change a child's name by Order of the Court, where for example an absent parent's whereabouts is unknown, but evidence would need to be provided to the Court of attempts made to contact the absent parent, together with details of how long the absent parent has had no contact, as well as details of how they are no longer a part of the child's life.
If you would like to change your name, we at Samuels Solicitor can help. We provide a fast, fixed fee service and will start working for you immediately that you instruct us.
If you would likea free discussion about how to change your name, and the fees involved, contact us today.


A choice of the Classic or the Sleek Training Knife.
This package is realy cool.
What you see is what you get. The shirts are of a good quality, they are not my first, I like them for hard training because they hold the sweat in, they are very comfortable and they fit perfect. What the knife makes so interesting for reality training is the weight. You take it and from the first moment on you get the feeling as if you hold a real knife. Spasibo Vladimir.
Whether you are new to Systema, or just want more Tees, this package is great value.
The training knife is very robust and well balanced, feeling very much like the real thing. Outstanding.


text:
case class Gear(name: String, enc: Double, cost: Int, am: Int = 1, own: Character = Character.NOBODY) extends Item(name, enc, cost, am, own) {

  def settle(am: Int, newowner: Character): Gear = {
    require(am < _amount)
    this.use(am)
    new Gear(this.name, this.enc, this.cost, am, newowner)
  }

}

redpajama_set_name: RedPajamaGithub


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The Huck-a-Bucks was a Washington, D.C.-based go-go band formed in the early 1990s. The band was active in the Washington metropolitan area, producing numerous songs in the Washington music scene and several hits nationwide, including the single "The Bud". The band members consisted of Joseph "Lil Joey" Timms rapping/singing, Charles "Ricky" Yancy, Lamont "Ray-Ray" Ray playing percussions, Rob "RJ" Folson, DeCarlos Cunningham, keyboardist Lorenzo Wiliams, drummer Felix Stevenson, and Sequan "Quan" Jones playing congas and percussions.

Discography

Albums
Chronic Breakdown (Liaison, 1995)
Live! (Liaison, 1995)
You Betta' Move Somethin'! (Sound By Charlie, 1997)

Songs
"Sexy Girl" (1995)
"The Bud" (1995)
"Kombat" (1995)
"Sprinkle" (1995)

References

External links
Huck-A-Bucks at AllMusic
Huck-A-Bucks at Last.fm

African-American musical groups
American funk musical groups
Go-go musical groups
Musical groups from Washington, D.C.

redpajama_set_name: RedPajamaWikipedia


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5 Darkest Dungeons in the World you can Visit – Guide
Posted on 23.07.2018 23.07.2018 by Renee Sylvanas
How about tickling your nerves during the holidays? Go down into the dungeons, where the horror picks up to the bones, and blows the sepulchral cold. Skeletons dressed in medieval caftans, bones stacked together and niches, forming altars … We present the darkest catacombs of Europe, where you can come with a guide.
Catacombs of Capuchins
The history of this strange cemetery began in the 16th century, when a monastic Order of Capuchins appeared in Sicily. The monks did not want to be buried away from their native monastery and built the cemetery right in the underground room – the crypt – under their own temple. After a while it turned out that the strange air in the catacombs does not allow the corpses to decompose. And then pre-dried and dressed up the local elite was buryed here. The cemetery was active until the end of the XIX century. During this time, the eight thousand Sicilians were buryed here. Lie corpses hang on the hooks on both sides of these underground passages – in the clothes in which they were brought here centuries ago.
Saint Solomon Catacombs
The entrance to the catacombs of Solomon is easy to learn, thanks to a nearby pistachio tree, hung with colorful rags, beads and kerchiefs: which are left by people who suffered from curing diseases. Initially, there was a city burial vault, which began to serve as a refuge for the first followers of the new religion with the advent of Christianity. But it did not save Solomonius and her seven sons from death, who were killed in front of her mother and buried here. In the underground labyrinths the ancient church preserved to nowadays, whose walls are painted with frescoes. There is a source in the catacombs with healing water, curing all ailments.
Read also: The commercial centers of the world, not to be missed if you love shopping
St. Paul Catacombs
The Maltese catacombs of St. Paul are more modestly tan Roman, there is no scope for the tragedy that Christians experienced at the beginning of their history. But you will not leave this place without any impression here. These underground rooms were covered with funeral meals, with lamps in small niches. According to the legend, the Apostle Paul prayed here, the one that allegedly sailed on the ship and crashed near the coast of Malta.
Kom el-Shugafa Catacombs
This is the Roman necropolis of the beginning of our era. The three-level labyrinth of tombs goes 35 meters under the ground. The ground floor is completely filled with water, the second floor is partially filled. One of the most interesting places is Triklinium. This is a refectory hall used by relatives of the deceased for the farewell ceremony. The most horrible is the hall of Caracalla, where a lot of people and animals were killed, killed by order of a cruel Roman emperor. The funerary chapel is painted with scenes of Christian funerals, the entrance to it is guarded by statues of the gods Sobek and Anubis in Roman armor.
Catacombs of Paris
Catacombs on the outskirts of Paris appeared when the city was intensively built up, and to much stone was needed for the construction of churches, houses and palaces. The catacombs were transformed in the underground cemetery in 1785-1810, when several million skeletons were lowered to the ground. They were brought here at night on carts from the Innocent Cemetery, located in the center of the city. The Parisian authorities took such a decision because of the fact that the land level increased to three meters due to numerous burial places , and it became a breeding ground for infections. Unerground workers stacked different parts of the skeletons apart from each other. So today you can see a wall, built up of tibia bones.
Read also: 35 Tips for Road Travelers


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Clearance of the C-spine in the unconscious patient
Topic: Neurology and Neurosurgery
Previous chapter: Management of acute high spinal injury
Next chapter: Important spinal cord injury syndromes
Given that this is a common and practical ICU problem, the college have wisely included it among their SAQs - Question 10 from the second paper of 2008 asks the candidate to "Outline and justify your approach to "clearing" the cervical spine in an adult multi-trauma patient with a severe closed head injury".
Since this question (written in 2008),
The Alfred published an evidence-based C-spine clearance protocol (2009)
Another edition of Oh's Manual was produced, incorprating some new evidence (though still mostly referencing studies published prior to 2008).
Patel et al published a set of guidelines: "Cervical Spine Collar Clearance in the Obtunded Adult Blunt Trauma Patient".
Question 14 appeared in the second paper of 2020, to ask the same question again (including about the complications of remaining in a collar for too long)
A synthesis of the abovelisted sources can be attempted, and rendered into this brief summary:
A normal result of a high-quality CT is enough to remove the collar.
Let us discuss this statement.
Clinical criteria:
Clinical criteria for C-spine clearance basically exist to help you decide when you need to send the patient for a CT of the neck. Ch.78 from Oh's Manual (Spinal injuries by Sumesh Arora and Oliver J Flower) make specific mention of the NEXUS criteria and the Canadian C-spine rules. Even though everybody is already well aware of them, they are reproduced below largely as a reference for the forgetful author:
Clinical C-spine Clearance Criteria
The NEXUS criteria
The C-spine CT is not required if there is :
• no posterior midline cervical spine tenderness
• no evidence of intoxication
• a normal level of alertness
• no focal neurological deficit
• no painful distracting injuries.
"an alert level of conscious-ness sufficient to allow three-object recall at 5 minutes" is required.
Not even the odour of alcohol is permitted.
"Distracting injury" is a fairly subjective criterion.
The Canadian Rules
The C-spine CT is not required if :
• The patient is under 65 years of age
• The mechanism was not "dangerous"
• There is no paraesthesia in the extremities
• The mechanism permits safe ROM assessment
• The patient is able to painlessly rotate their head 45°
Sensitivity: 99.6% for significant injuries
Specificity: 12.9%.
Sensitivity: 100% for significant injuries
Specificity: 45%.
Flower and Arora reference this NEJM article from 2003 as a source for their discussion of the various C-spine rules. It is therefore probably worth reading. However, before the time-poor candidate commits themselves to a thorough exploration of the C-spine controversy, it would be important to mention that emergency departments routinely pan-scan their multitrauma patients, and the C-spine ends up getting caught in the radiation beam because "while you're there" and "that injury looks distracting" and "he's drunk and crazed with meth and we intubated him". So, for the intensivist, the question is rarely "does this patient need a CT", and frequently "when can we take the collar off".
To launch into the above-advertised thorough exploration of C-spine clearance rules, the NEXUS criteria are a good start. NEXUS stands for National Emergency X-Radiography Utilization Study, a prospective observational study of 34,069 patients published in NEJM by Hoffman et al (2000). The study tested the validity of five criteria for the exclusion of cervical spine injury: midline tenderness, altered mental state, intoxication, focal neurodeficit and distracting injury. These criteria were not explicitely defined; for example each participating centre was left to determine what constitutes a painful distracting injury. The NEXUS investigators then performed C-spine Xrays on all the patients. It turned out the NEXUS criteria were fairly sensitive. A radiologically apparent injury was missed only in 8 of the 818 patients who had significant C-spine trauma.
The Canadian rules are a slightly different set of criteria published by Stiell et al (2001). The authors prospectively observed 8924 patients. Instead of testing an already acknowledged list of criteria like the NEXUS authors, the Canadian group looked at 20 different clinical findings and compared their predictive value in excluding C-spine injury. By these rules, anybody with an age over 65, with a dangerous mechanism of injury, the presence of a sensory deficit or something preventing range of motion testing will get a CT by default. If you had a simple rear-end MVA, were sitting upright in the emergency department, were found ambulant at the scene of the accident, or had no neck pain - you could easily have ROM testing, and being able to actively and painlessly rotate the neck 45 degrees in either direction was 100% sensitive for the absence of a C-spine injury.
So which set of criteria is the better, or are they both the same? There appears to be only one direct comparison of NEXUS vs. Canadian rules (by the same guy who published the original Canadian rules paper - Ian Stiell et al, 2003). A 2012 review by Michaleff et al did not manage to find any others, but compared a whole series of data sets that validated a set of criteria independently. On their analysis, the authors found that the Canadian rules were slightly better. The sensitivity for both sets of rules was superb but the Canadian rules had a subtle advantage (the difference being 99.6% vs 100% sensitivity). Both sets of criteria have the distinct disadvantage of producing a lot of unnecessary imaging, but the Canadian rules are slightly less likely to cause inappropriate irradiation (they reduced imaging rates to 55.9%, as compared to 66.6% for the Nexus criteria). Given that we have these clinical criteria mainly because we do not want to scan everybody, a reduced imaging rate is an important performance characteristic.
Disadvantages of being in a C-spine collar
There are certain problems with being an immobile trauma victim trapped inside a stiff neck collar, with restrictions on how you can be turned for routine care, and how your torso can be positioned.
A 2004 review by Morris and McCoy (quoted in Oh's Manual) presents a list of disadvantages as Figure 1, which is summarised below with some modification:
Problems associated with prolonged C-spine immobilisation
Pressure areas under the collar
Source of sepsis
Need for skin grafts
Increased hospital stay
Increased intracranial pressure
Airway is made more difficult by in-line stabilisation
Central venous access is made more difficult (IJ is out of bounds)
Oral care is made more difficult, increasing the risk of VAP
Nutrition is affected:
Gastroparesis and ileus results from prolonged immobility
Aspiration risk is increased by supine position
Physiotherapy is delayed or impossible
A greater risk of DVT/PE results from prolonged immobility
A minimum of 4 nursing staff are required to turn the patient.
None of these issues are going to sound surprising. Perhaps the reason these problems are neglected is that missed C-spine injuries are easy substrate for big public medicolegal spectacle, while a series of non-sexy complications like DVTs and bedsores are much less attractive to the media.
The Australian experience: when can we take the collar off?
According to a 2003 article, back then we didn't have a good standard way of doing this, and nobody was sure whether this was causing people harm. Lien Jaques and Powell lament:
"There is no standardised approach to the clearance of the cervical spine in intubated trauma patients in Australian intensive care units. In addition, morbidity from current practices and the true incidence of cervical spine injuries remains unknown."
So, in 2005 Cooper and Ackland published a summary which was good enough for the college to include on their website. In it, they discuss the evidence-based protocol they use at The Alfred. This cannot be a terrible protocol to follow, as it has been used as the source for at least one fellowship exam question. The specific feature of this is the simplicity of the algorithm they use for the unconscious patient. If the CT is normal, they clear the C-spine. Simple as that.
However, bold all-caps writing across their flowchart recommends that removing the collar in this context is a CONSULTANT-SUPPORTED DECISION, which I interpret as a warning. Any trainee clearing the C-spine from CT all by themselves will find themselves medicolegally exposed; more so if they aren't actually practicing at the Alfred. The reason for this is highlighted succinctly by the 2015 EAST guidelines: "the use of this approach may result in a nonzero rate of neurologic deterioration".
The implication, of course, is that in pursuit of a "zero rate" one ends up generating a nonzero rate of complications due to prolonged immobilisation, repeated scan transfers, unnecessary treatments and misguided specialist referrals.
The value of the trauma series CT in excluding spinal injury
It picks up 97% of bony injuries
It picks up 86% of subluxation injuries
It misses 75% of ligamenous injuries
It misses 100% (!!) of spinal cord injuries
However, a recent (2010) prospective study has concluded that for all its disadvantages, the CT picks up 99.75% of clinically significant spinal cord injuries. Yes, in other studies MRI found all sorts of extra ligamentous injuries whcih the CT had missed, but none of these were clinically significant, so why delay removing the collar?
When is it appropriate to use MRI to image the C-spine
There are a few features which would prompt you to order an MRI:
Signs or symptoms of spinal cord injury
The CT suggests there is ligamentous injury (or injury to the disc)
The reluctance of guideline-makers to greater integration of MRI into guidelines stems from the expense and poor availability of MRI, and from the risk of MRI transfer for the severely injured multi-trauma patient. Additionally, MRI can have a rate of false positives as high as 40%, resulting in the development of a large chronically C-collared population. If you are going to do it, then you should do it reasonably soon: after 72 hours, the gradual decrease in ligamentous oedema may increase the false-negative rate.
Is there any role for flexion-extension C-spine views
In this enlighetend age of iPhones and high-resolution helical CT scanners and whatnot, the humble flexion-extension C-spine film has fallen into disuse. So much has it become surpassed in diagnostic value, that some call for its immediate shamed expulsion from current C-spine management protocols. This view is supported by evidence. A 2013 systematic review of many heterogeneous studies has concluded that wherever CT and MRI are available, the value of this practice is minimal.
The Alfred Spinal Clearance Protocol
Chapter 78 (pp. 795) Spinal injuries by Sumesh Arora and Oliver J Flower
Lien, D., T. Jacques, and K. Powell. "Cervical spine clearance in Australian intensive care units." Critical Care and Resuscitation 5.2 (2003): 91.
Cooper, D. J., and H. M. Ackland. "Clearing the cervical spine in unconscious head injured patients-the evidence." Critical Care and Resuscitation 7.3 (2005): 181.
Hennessy, Deirdre, et al. "Cervical spine clearance in obtunded blunt trauma patients: a prospective study." The Journal of Trauma and Acute Care Surgery68.3 (2010): 576-582.
Como, John J., et al. "Is magnetic resonance imaging essential in clearing the cervical spine in obtunded patients with blunt trauma?." Journal of Trauma-Injury, Infection, and Critical Care 63.3 (2007): 544-549.
Tran, Baotram, Jonathan M. Saxe, and Akpofure Peter Ekeh. "Are flexion extension films necessary for cervical spine clearance in patients with neck pain after negative cervical CT scan?." Journal of Surgical Research 184.1 (2013): 411-413.
Sierink, J. C., et al. "Systematic review of flexion/extension radiography of the cervical spine in trauma patients." European journal of radiology 82.6 (2013): 974-981.
Patel, Mayur B., et al. "Cervical spine collar clearance in the obtunded adult blunt trauma patient: A systematic review and practice management guideline from the Eastern Association for the Surgery of Trauma." Journal of Trauma and Acute Care Surgery 78.2 (2015): 430-441.
Morris, C. G. T., and E. McCoy. "Clearing the cervical spine in unconscious polytrauma victims, balancing risks and effective screening." Anaesthesia 59.5 (2004): 464-482.
Richards, Paula J. "Cervical spine clearance: a review." Injury 36.2 (2005): 248-269.
Hoffman, Jerome R., et al. "Validity of a set of clinical criteria to rule out injury to the cervical spine in patients with blunt trauma." New England Journal of Medicine 343.2 (2000): 94-99.
Stiell, Ian G., et al. "The Canadian C-spine rule versus the NEXUS low-risk criteria in patients with trauma." New England Journal of Medicine 349.26 (2003): 2510-2518.
Stiell, Ian G., et al. "The Canadian C-spine rule for radiography in alert and stable trauma patients." Jama 286.15 (2001): 1841-1848.
Jo, Alexandria S., et al. "Essentials of spine trauma imaging: radiographs, CT, and MRI." Seminars in Ultrasound, CT and MRI. Vol. 39. No. 6. WB Saunders, 2018.
Malhotra, Ajay, et al. "Utility of MRI for cervical spine clearance in blunt trauma patients after a negative CT." European radiology 28.7 (2018): 2823-2829.


text:
\section{Introduction}\label{sec:intro}
When  nuclear degrees of freedom (DoF) are allowed to fluctuate in the presence of a continuum of electronic DoFs, not only will the electronic wave function change at different nuclear positions (in accordance with the Born-Oppenheimer picture) --- the nuclear wave packet will also change as it receives feedback from the electronic DoF.
In the adiabatic limit, the
electronic feedback on the nuclei is composed of three parts: the adiabatic force $F_{\mu}$, the random force $\delta F_{\mu}$, and the frictional damping force. The friction tensor $\gamma_{\mu\nu}$ captures the strength of the nuclear damping force in the $\mu$-direction as caused by nuclear motion in the $\nu$ direction and reflects how fast electronic transitions inevitably interfere with simple nuclear (Newtonian) motion. Mathematically, the nuclei follow a stochastic Langevin equation\cite{van1992stochastic,dou2017born} of the form,
\begin{align}
M_{\mu}\ddot{R}_{\mu}=F_{\mu}-\sum_{\nu}\gamma_{\mu\nu}\dot{R}_{\nu}+\delta F_{\mu},\label{eq:langevin_eq}
\end{align}
where $M_{\mu}$ is the mass of a nuclei and $R_{\mu}$ is the nuclear position in the $\mu$ direction.

Several important general properties (and proofs) about $\gamma_{\mu\nu}$, including the positive definiteness and the fluctuation-dissipation theorem, are provided in SM \ref{si:review_ft}-\ref{si:no_gamma_A_for_real_H_equil}. Historically, electronic friction was first considered as a first-order correction to the Born-Oppenheimer approximation for dynamics near a metal surface, and though there have been many separate approaches for calculating the electronic friction tensor\cite{suhl:1975:prl_elfriction, suhl:1975:prb_elfriction,tully:1995:electronic_friction,brandbyge:1995:elfriction,dundas:2012:prb_berry,persson:2005:friction_noncondon, persson:2007:friction_noncondon,hynes:1993:elfriction,langreth:1999:prb_elfriction,langreth:1998:prb_elfriction,mozyrsky:2006:elfriction,mozyrsky:2007:pre_friction,lu2010blowing,bode2012current,chen2018current,dou2017born,galperin:2015:friction,dou2018perspective,lu2019semi}, all agree in the Markovian limit\cite{dou2017born}.
$\gamma_{\mu\nu}$ can be divided into a symmetric part $\gamma_{\mu\nu}^{\mathrm{S}}$ and an antisymmetric part $\gamma_{\mu\nu}^{\mathrm{A}}$. For a system at equilibrium, $\gamma_{\mu\nu}^{\mathrm{S}}$ is positive definite; this term can only dissipate energy to the surroundings (and avoid unstable dynamics). Such relaxation processes have been reported as important for molecule-metal interface dynamics (scattering, adsorption etc.)\cite{huang2000observation,huang2000vibrational,bunermann2015electron,rittmeyer2018energy}, electron transfer within electronic devices\cite{pop2010energy}, and heating due to the phonon motion\cite{koch2004thermopower,kaasbjerg2013charge}.  The diagonal component ($\mu=\nu$) can significantly change the electron-hole pair induced vibrational lifetime\cite{juaristi:2008:prl_ldfa,reuter:2015:prl_ldfa}, and the off-diagonal elements of a symmetric friction tensor ($\mu\neq\nu$)  can also be crucial\cite{askerka2016role,maurer2016ab}.

We have far less experience with the antisymmetric component of the friction tensor, $\gamma_{\mu\nu}^{\mathrm{A}}$, which contributes a Lorentz-like force.
Within the chemical physics condensed matter community, the usual assumption is that $\gamma_{\mu\nu}^{\mathrm{A}} = 0$ at equilibrium. That being said, for a strictly real-valued Hamiltonian describing a typical molecule on a typical metal, von Oppen and others\cite{lu2010blowing,bode2012current} have demonstrated that $\gamma_{\mu\nu}^{\mathrm{A}}\ne0$ only when molecules are in contact with two metals that are {\em out of} equilibrium (i.e. with a current).

Now, within the description above\cite{lu2010blowing,bode2012current}, there has been the assumption of a strictly real-valued  Hamiltonian. However, for molecule-metal interfaces or for surface heterostructures, due to the short electron screening length of a metal, the effective electric field gradient on the surface should lead to strong Rashba spin-orbit coupling\cite{manchon2015new}. Furthermore, a built-in molecular spin-orbit coupling can be enhanced due to molecular geometry, i.e. molecules with large curvature or torsion in geometry are believed to have larger spin-orbit coupling\cite{ando2000spin,huertas2006spin}. For these reasons,
{\em a complex-valued Hamiltonian may be quite relevant.} Moreover, Robbins and Berry have demonstrated that antisymmetric (Berry) forces may appear if the Hamiltonian is complex-valued\cite{berry1993chaotic}. Exact scattering calculations have shown that, for a closed model complex-valued Hamiltonian, the resulting Berry force effects can be large and strongly  affect electron transfer processes\cite{miao2019extension}.

Where does this leave us as far as understanding molecular dynamics near a metal surface? For the most part, a molecule on a metal surface is occupied by a fractional number of electrons; as electrons are shared between molecule and metal, the molecular nuclei will feel different forces depending on the fluctuating electronic charge state.  While such fluctuations are known to lead to fast vibrational relaxation of a diatomic on a metal surface\cite{huang2000vibrational} through the symmetric tensor, one can ask: Does a significant nonzero antisymmetric friction tensor (i.e. a pseudomagnetic field) also appear when we consider a complex-valued Hamiltonian describing a molecule near a metal surface in equilibrium?
Note that, except for a few analogous examples in the realm of spintronics\cite{bajpai2020spintronics}, to date, the effect of a magnetic field or spin-orbit coupling has been ignored in friction tensor calculations (even though $\gamma_{\mu\nu}$ is general). Note also that Ref. \citenum{wu2021electronic} predicts that  a huge Berry force can be generated for an isolated molecular system near a sharp avoided crossing in the presence of spin-orbit coupling.
One must wonder whether such a huge Berry force will still exist when one considers a molecule strongly coupled to a metal surface.

Below, we will address these questions. In particular, we will show that: (i) Like the case of an isolated molecular system, a Berry force exists whenever a molecular system with a complex-valued Hamiltonian is coupled to a bath (no matter whether or not the total system is in \textit{equilibrium}). (ii) Unlike the case of an isolated molecular system, the strength of the Berry force does not require a tiny energy gap (i.e. a sharp avoided crossing) to achieve a large Berry force (in fact an energy gap is necessary). (iii) $\gamma_{\alpha\nu}^{\mathrm{A}}$ is comparable or can even be one order of magnitude larger than $\gamma_{\mu\nu}^{\mathrm{S}}$ and thus affects the experimental observable. These facts suggest that nuclear motion at surfaces should promote certain flavor of electronic spin selectivity, e.g. perhaps spin selectivity in transport with chiral molecules.

\section{Model System}\label{sec:model_sys}
We consider a model in which a two-level system is coupled to two leads and the two-level system depends on two dimensional nuclear DoF. While there is an immense amount known about the (symmetric) friction tensor that arises for a resonant level model\cite{bode2012current,chen2019electronic}, no such results or intuition have been derived for the antisymmetric friction tensor even in the case of a two-level model at equilibrium.

Here we will derive the friction tensor analytically. The total electronic Hamiltonian $\hat{H}$ is divided into three components, the system $\hat{H}_{\mathrm{s}}$, the bath $\hat{H}_{\mathrm{b}}$ and the system-bath coupling $\hat{H}_{\mathrm{c}}$:
\begin{align*}
\hat{H}=&\hat{H}_{\mathrm{s}}+\hat{H}_{\mathrm{b}}+\hat{H}_{\mathrm{sb}},\\
\hat{H}_{\mathrm{s}}=&\sum_{mn}h^{\mathrm{s}}_{mn}(\mathbf{R})\hat{b}_{m}^{\dagger}\hat{b}_{n}+U(\mathbf{R}),\\
\hat{H}_{\mathrm{b}}=&\sum_{k\alpha}\epsilon_{k\alpha}\hat{c}_{k\alpha}^{\dagger}\hat{c}_{k\alpha},\\
\hat{H}_{\mathrm{c}}=&\sum_{m,k\alpha}V_{m,k\alpha}\hat{b}_{m}^{\dagger}\hat{c}_{k\alpha}+\mathrm{H.c.}
\end{align*}
Above, $m$, $n$ label system orbitals, and $\hat{b}_{m}^{\dagger}$ ($\hat{b}_{m}$) creates (annihilates) an electron in the system orbital $m$. $\hat{c}_{k\alpha}^{\dagger}$ ($\hat{c}_{k\alpha}$) creates (annihilates) an electron in the $k$-th orbital of a lead $\alpha$.  Note that, for the sake of generality,
all expressions below will be derived for the case of two electronic leads; $\alpha=\mathrm{L},\mathrm{R}$ indicates left and right leads.  If we set the fermi levels $\mu_{\alpha}$ of both leads to be equal, $\mu_{\mathrm{L}} = \mu_{\mathrm{R}}$, there is no difference between having
one lead (with $2N$ orbitals) or two leads (with $N$ orbitals).
$h^{\mathrm{s}}_{mn}$ is the molecular electronic  Hamiltonian  that depends explicitly on $\mathbf{R}$, the molecular nuclear DoFs,
and we know that this dependence on $\mathbf{R}$  leads to a symmetric friction tensor\cite{dou2017born}. $U(\mathbf{R})$ is a pure nuclear potential energy. $V_{m,k\alpha}$ represents the tunneling element between the system orbital $m$ and the lead orbital $k\alpha$,
which we assume independent of $\mathbf{R}$ (the so-called Condon approximation). Within this model, the most general system Hamiltonian can be written in Pauli matrices representation ($\sigma_{i}$\cite{pauli_representations}) as:
\begin{align*}
\mathbf{h}^{\mathrm{s}}=\mathbf{h}(x,y)\cdot\bm{\sigma}=\sum_{i=1,2,3}h_{i}(x,y)\sigma_{i},
\end{align*}
where $\lbrace h_{i}\rbrace$ is real. Note that the inclusion of $h_{2}$ makes the Hamiltonian possibly complex-valued, as might arise from an external magnetic field or spin-orbit coupling.

If we now evaluate $\gamma_{\mu\nu}$ for the case of non-interacting electrons (following Ref. \citenum{dou2018universality}; $\hbar=1$), we find that the (exact) final results is (see SM \ref{si:review_ft}):
\begin{align}
\gamma_{\mu\nu}=\int\frac{d\epsilon}{2\pi}\Tr{\partial_{\mu}h^{\mathrm{s}}\partial_{\epsilon}\Ropt{G}\partial_{\nu}h^{\mathrm{s}}G^{<}}+\mathrm{H.c.},\label{eq:ft_non_condon}
\end{align}
where $\Ropt{G}=(\epsilon-h^{\mathrm{s}}-\Ropt{\Sigma})^{-1}$ is the (two-level) system retarded Green's function, $\Ropt{\Sigma}_{mn}=\sum_{k\alpha}V_{m,k\alpha}\Ropt{g}_{k\alpha}V^{*}_{n,k\alpha}$ is the system self energy, and $\Ropt{g}_{k\alpha}=(\epsilon-\epsilon_{k\alpha}+i\eta)^{-1}$ is the lead retarded self energy ($\eta\rightarrow0^{+}$). $G^{<}$ is the system lesser Green's function and, provided that an imaginary surrounding is quadratic\cite{dou2018universality} or the system spectral broadening due to the leads is finite\cite{haug2008quantum}, $G^{<}$ can be calculated by the Keldysh equation, $G^{<}=\Ropt{G}\Sigma^{<}\Aopt{G}$. Here $\Sigma^{<}_{mn}=\sum_{k\alpha}V_{m,k\alpha}g^{<}_{k\alpha}V_{n,k\alpha}^{*}$ is the system lesser self energy, and $g^{<}_{k\alpha}(\epsilon)=i2\pi f_{\alpha}(\epsilon)\delta(\epsilon-\epsilon_{k\alpha})$ is the lead lesser Green's function. ($f(\epsilon)=1/[\exp{(\beta(\epsilon-\mu))}+1]$ is the Fermi-Dirac distribution with the inverse temperature $\beta$ and the chemical potential $\mu$.)

We further make the following standard assumptions\cite{stefanucci2013nonequilibrium}: (i) the tunneling-width matrix $\Gamma_{mn}=2\pi\sum_{k\alpha}V_{m,k\alpha}V_{n,k\alpha}^{*}\delta(\epsilon-\epsilon_{k\alpha})$ is independent of $\epsilon$ (i.e. the wide band limit approximation), (ii) $\Gamma_{mn}=\tilde{\Gamma}$ is a constant, (iii) the tunneling elements $V_{m,k\alpha}$ are independent of $k$, and (iv) the left lead couples only to orbital $1$ and the right lead couples only to orbital $2$, with the two coupling constants the same real value. Therefore,
$\Ropt{\Sigma}=-\frac{i}{2}\tilde{\Gamma}$, and $\Sigma^{<}=i\tilde{\Gamma}\left(f_{\mathrm{L}}\,0;\,0\,f_{\mathrm{R}}\right)$ where $f_{\mathrm{L}}$ and $f_{\mathrm{R}}$ are Fermi-Dirac distribution of the left and right leads respectively. Please see SM \ref{si:schematic_pic} for a schematic picture (equilibrium case).

A calculation (see SM \ref{si:ft_calculation_details}) shows that the friction tensor (from Eq. (\ref{eq:ft_non_condon})) is,
\begin{alignat}{2}
\gamma_{\mu\nu}=&\gamma_{\mu\nu}^{\mathrm{S}}+\gamma_{\mu\nu}^{\mathrm{A}},\label{eq:ft_tls}\\
\gamma_{\mu\nu}^{\mathrm{S}}=&\frac{2}{\pi}\int_{-\infty}^{\infty}d\epsilon\bigg\{&&-2\mathfrak{Re}\left\{C\tilde{\epsilon}\right\}\left(\partial_{\mu}\mathbf{h}\cdot\partial_{\nu}\mathbf{h}\right)\left(\mathbf{h}\cdot\bm{\kappa}\right)\notag\\
&&&+2\mathfrak{Re}\left\{C\tilde{\epsilon}\right\}\left(\partial_{\mu}\mathbf{h}\cdot\mathbf{h}\right)\left(\partial_{\nu}\mathbf{h}\cdot\bm{\kappa}\right)\notag\\
&&&+2\mathfrak{Re}\left\{C\tilde{\epsilon}\right\}\left(\partial_{\nu}\mathbf{h}\cdot\mathbf{h}\right)\left(\partial_{\mu}\mathbf{h}\cdot\bm{\kappa}\right)\notag\\
&&&+\kappa_{0}\mathfrak{Re}\left\{C\left(\tilde{\epsilon}^{2}+h^{2}\right)\right\}\partial_{\mu}\mathbf{h}\cdot\partial_{\nu}\mathbf{h}\bigg\}\label{eq:ft_tls_sym}\\
\gamma_{\mu\nu}^{\mathrm{A}}=&\frac{2}{\pi}\int_{-\infty}^{\infty}d\epsilon\bigg\{&&-\mathfrak{Im}\left\{C\left(\tilde{\epsilon}^{2}+h^{2}\right)\right\}
\bm{\kappa}\cdot\left(\partial_{\mu}\mathbf{h}\times\partial_{\nu}\mathbf{h}\right)\notag\\
&&&+2\kappa_{0}\mathfrak{Im}\left\{C\tilde{\epsilon}\right\}\mathbf{h}\cdot\left(\partial_{\mu}\mathbf{h}\times\partial_{\nu}\mathbf{h}\right)\bigg\},\label{eq:ft_tls_antisym}
\end{alignat}
Here
\begin{align*}
C\equiv-\left(\frac{1}{\tilde{\epsilon}^{2}-h^{2}}\right)^{2}i\tilde{\Gamma}\@ifstar{\oldabs}{\oldabs*}{\frac{1}{\tilde{\epsilon}^{2}-h^{2}}}^{2},
\end{align*}
where $\tilde{\epsilon}=\epsilon+i\tilde{\Gamma}/2$ is a complex number, and $h^{2}=\mathbf{h}\cdot\mathbf{h}$. The $\kappa$'s are defined as
\begin{align*}
\kappa_{0}=&\frac{1}{2}\left[\left(f_{\mathrm{L}}+f_{\mathrm{R}}\right)\left(h_{1}^{2}+h_{2}^{2}\right)+f_{\mathrm{L}}\@ifstar{\oldabs}{\oldabs*}{\tilde{\epsilon}+h_{3}}^{2}+f_{\mathrm{R}}\@ifstar{\oldabs}{\oldabs*}{\tilde{\epsilon}-h_{3}}^{2}\right],\\
\kappa_{1}=&\mathfrak{Re}\left\{\left[f_{\mathrm{L}}\left(\tilde{\epsilon}^{*}+h_{3}\right)+f_{\mathrm{R}}\left(\tilde{\epsilon}-h_{3}\right)\right]\left(h_{1}+ih_{2}\right)\right\},\\
\kappa_{2}=&\mathfrak{Im}\left\{\left[f_{\mathrm{L}}\left(\tilde{\epsilon}^{*}+h_{3}\right)+f_{\mathrm{R}}\left(\tilde{\epsilon}-h_{3}\right)\right]\left(h_{1}+ih_{2}\right)\right\},\\
\kappa_{3}=&\frac{1}{2}\left[\left(f_{\mathrm{R}}-f_{\mathrm{L}}\right)\left(h_{1}^{2}+h_{2}^{2}\right)+f_{\mathrm{L}}\@ifstar{\oldabs}{\oldabs*}{\tilde{\epsilon}+h_{3}}^{2}-f_{\mathrm{R}}\@ifstar{\oldabs}{\oldabs*}{\tilde{\epsilon}-h_{3}}^{2}\right].
\end{align*}
Note that $\kappa_{0}$ and $\bm{\kappa}=(\kappa_{1},\kappa_{2},\kappa_{3})$ are real functions. When the total system is in equilibrium, namely $f_{\mathrm{L}}=f_{\mathrm{R}}=f$,
\begin{align}
\kappa_{0}=&f\left(\epsilon^{2}+h^{2}+\frac{\Gamma^{2}}{4}\right),\label{eq:condition1_at_equil}\\
\bm{\kappa}=&2f\epsilon\mathbf{h}.\label{eq:condition2_at_equil}
\end{align}
Equations (\ref{eq:ft_tls})-(\ref{eq:ft_tls_antisym}) represent a very general electronic friction tensor for a minimal model of a molecule near metal surfaces in the presence of spin-orbit coupling.

\section{Results and Discussions}\label{sec:results_n_discussions}
According to Eq. (\ref{eq:ft_tls}) we can make two important and general conclusions regarding Berry forces of equilibrium near a metal surface.
First, according to Eqs (\ref{eq:ft_tls_antisym})-(\ref{eq:condition1_at_equil}), $\gamma_{\mu\nu}^{\mathrm{A}}$ is proportional to $\mathbf{h}\cdot\left(\partial_{\mu}\mathbf{h}\times\partial_{\nu}\mathbf{h}\right)$. Therefore, $\gamma_{\mu\nu}^{\mathrm{A}}$ will vanish when at least one element of $\mathbf{h}$ is zero, or when two elements of $\mathbf{h}$ are the same. These facts demonstrate not only that an imaginary off-diagonal coupling ($h_{2}$) is required for a nonzero $\gamma_{\mu\nu}^{\mathrm{A}}$, but also that the key source of a nonzero $\gamma_{\mu\nu}^{\mathrm{A}}$ is the spatial dependence of the phase of the off-diagonal coupling, $\tan^{-1}{(h_{2}/h_{1})}$. After all, if $h_{1}=0$ or $h_{1}(x,y)=h_{2}(x,y)$, we can find a constant change of basis transformation
that guarantees a globally real-valued Hamiltonian and therefore $\gamma_{\mu\nu}^{\mathrm{A}}=0$. In other words, in such a case, there is no Lorentz-like force.

Second, according to Eqs. (\ref{eq:ft_tls})-(\ref{eq:condition2_at_equil}), one can construct several nonequivalent Hamiltonians that generate equivalent friction tensors. To see this, note that, when the system is in equilibrium, the symmetric terms in Eq. (\ref{eq:ft_tls}) all have dot product dependence on $\mathbf{h}$, namely $h^{2}$, $\sum_{i}\partial_{\mu}h_{i}\partial_{\nu}h_{i}$ and $\sum_{i}\partial_{\mu}h_{i}h_{i}$. Thus, the symmetric terms are invariant to any permutation of $\mathbf{h}=\{h_{1},h_{2},h_{3}\}$. Moreover, the two terms comprising $\gamma_{\mu\nu}^{\mathrm{A}}$ depend on $\mathbf{h}\cdot(\partial_{\mu}\mathbf{h}\times\partial_{\nu}\mathbf{h})$, which are also invariant under cyclic permutation of the $\mathbf{h}$ elements. Thus, different Hamiltonians can generate the same friction tensor and, as a practical matter, this must have experimental consequences as some Hamiltonians are undoubtedly easier to realize than others. For example, in Eq. (\ref{eq:hs_ft}) we will consider a model Hamiltonian with diagonal coupling $h_{3}=x+\Delta$; here, as in standard Marcus theory, $\Delta$ is a driving force that will be shown to play an important role in generating a
large antisymmetric friction tensor. Nevertheless, if ones imagines permuting the $\mathbf{h}$ elements by substituting $h_{1}\rightarrow h_{3}\rightarrow h_{2}$, then the parameter $\Delta$ will enter on the off-diagonal of the Hamiltonian and can be realized, e.g., by tuning an external magnetic field.

These are the only direct, general conclusions we can make from Eqs. (\ref{eq:ft_tls})-(\ref{eq:condition2_at_equil}). Next, let us focus on a model problem which can yield further insight using numerical analysis. We imagine the standard case of two shifted parabolas, expressed in a nuclear space with two dimensions and with a driving force of $2\Delta$. Mathematically, the system Hamiltonian is taken to be of the form:
\begin{align}
\mathbf{h}^{\mathrm{s}}=
\begin{pmatrix}
x+\Delta & Ax-iBy\\
Ax+iBy & -x-\Delta
\end{pmatrix},\label{eq:hs_ft}
\end{align}
and $U=x^{2}/2+y^{2}/2+1/2$. We calculate the electronic friction tensor by using Eq. (\ref{eq:ft_tls}). Note that the pure nuclear potential $U$ does not contribute to the friction tensor. Recall that $\gamma_{\mu\nu}^{\mathrm{A}}\propto\mathbf{h}^{\mathrm{s}}\cdot(\partial_{\mu}\mathbf{h}^{\mathrm{s}}\times\partial_{\nu}\mathbf{h}^{\mathrm{s}})=AB\Delta$.  Thus, as argued above, if there is no change in the phase of the off-diagonal coupling ($A=0$ or $B=0$) in the nuclear space, we will find that $\gamma_{xy}^{\mathrm{A}}=0$. Also notice that when the driving force $\Delta=0$, again $\gamma_{\mu\nu}^{\mathrm{A}}=0$.  Beyond these two extreme cases, we will find both symmetric and antisymmetric components of the friction tensor.

\begin{figure}[!h]
\centering
\includegraphics[width=.5\textwidth]{fig2}
\caption{Friction tensor calculation results: $\gamma_{xx}$ (top left), $\gamma_{xy}^{\mathrm{S}}$ (top right), $\gamma_{xy}^{\mathrm{A}}$ (bottom left) and $\gamma_{yy}$ (bottom right). Parameters: $\tilde{\Gamma}=1$, $\mu_{\mathrm{R}}=\mu_{\mathrm{L}}=0$, $\beta=2$, $A=1$, $B=1$, $\Delta=3$. Notice that all the results in Figs. \ref{fig:D3} and \ref{fig:b2_D3} have mirror symmetry about $x=-1.5=-\Delta/(A^{2}+1)$ and $y=0$, because all six terms in Eq. (\ref{eq:ft_tls_sym}) and Eq. (\ref{eq:ft_tls_antisym}) are functions of $[x+\Delta/(A^{2}+1)]^{2}$ and $B^{2}y^{2}$ when the system is in equilibrium.\label{fig:b2_D3}}
\end{figure}

In Fig. \ref{fig:b2_D3}, we show contour plots for the friction tensor with $\beta=2$, $A=B=1$. Here, $A=B$ corresponds to a strong change of phase in the off-diagonal coupling. Several features are clear from the contour plot. First, the antisymmetric friction tensor $\gamma_{xy}^{\mathrm{A}}$ is one order larger than all other symmetric friction tensors. Thus, clearly Lorentz-like motion can be as important as any dissipative process. Second, the magnitude of $\gamma_{xy}^{\mathrm{A}}$ is maximized around the avoided crossing at $(-1.5,0)$, but for each component of the symmetric friction tensor, the magnitude is maximized far from the avoided crossing. Therefore, depending on the preparation of the initial nuclear wave packet, one might imagine that slow nuclei will equilibrate before feeling any Lorentz like force. That being said, the exact details for any calculation must be evaluated on a case-by-case basis.

\begin{figure}[!h]
\centering
\includegraphics[width=.5\textwidth]{fig3}
\caption{Friction tensor calculation results (only $\gamma_{xx}$ and $\gamma_{xy}^{\mathrm{A}}$ are shown). Parameters for (a) and (b) are $\tilde{\Gamma}=1$, $\mu_{\mathrm{R}}=\mu_{\mathrm{L}}=0$, $\beta=2$, $A=0.05$, $B=1$, $\Delta=3$; (c) and (d) have the same parameters as (a) and (b), except that $A=0.01$.\label{fig:b2_D3_A005}}
\end{figure}

In Fig. \ref{fig:b2_D3_A005}, we further investigate how the relative strength of the antisymmetric friction tensor changes as a function of
how the off-diagonal coupling changes phase. Here we keep the same parameters as in Fig. \ref{fig:b2_D3}, except we change $A$. In subplots (a)(b), the antisymmetric friction tensor $\gamma_{xy}^{\mathrm{A}}$ has the same order of magnitude as the symmetric friction tensors. In subplots (c)(d), we reduce $A$ so that $A=0.01$; we find the antisymmetric friction tensor approaches zero rapidly. We conclude that in \textit{any} theoretical or experimental works which consider an external magnetic field or/and spin-orbit coupling with reasonable changes for the phase (here larger than $5\%$) in the nuclear space, we cannot ignore the effect of the antisymmetric friction tensor. We have also performed several \textit{ab initio} calculations so as to extract parameters for a real system --- a diphenylmethane junction (See SM \ref{si:diphenylmethane}). The results are consistent with the conclusion above --- even when spin-orbit coupling is small, $\gamma_{xy}^{\mathrm{A}}$ can still be dominant.

Lastly, before concluding, we summarize a few results that are addressed
in the SM. First, we investigate the dependence of $\gamma^{\mathrm{S}}$ and $\gamma_{\mathrm{A}}$ on $\beta$ and $\tilde{\Gamma}$ in SM \ref{si:ft_T_effect} and SM \ref{si:ft_other_results} respectively. We find that the relative strength of $\gamma_{xy}^{\mathrm{A}}$ grows stronger for lower temperatures. Also, when the system-bath coupling strength $\tilde{\Gamma}$ grows very large, both the symmetric and antisymmetric friction tensors become smaller and these tensors are nonzero over an effectively smaller portion of nuclear configuration space. Second, while we have considered an avoided crossing above, in SM \ref{si:ci} we investigate true complex-valued conical intersections. There, we show that the dynamical effect of a pseudomagnetic field in the direct vicinity of a true conical intersection is likely not very large. Third, and most importantly, throughout this letter, we have focused mostly on the magnitude of the antisymmetric friction tensor. Note that, in a basis of spin orbitals, switching spin up and spin
down orbital will swap $h_{2}$ and $-h_{2}$ and lead to different signs of $\gamma_{\mu\nu}^{\mathrm{A}}$. Thus, different spins will feel different directions of the Lorentz force and the present formalism may underlie spin selectivity for molecular processes near metal surfaces\cite{naaman:2011:science:ciss_dna,naaman:2019:natrev,zollner2020insight}. As a practical matter if we were to construct an overall electronic friction tensor for the case of a system with multiple spin degrees of freedom, such a tensor would be meaningful only when the spin degrees of freedom interconvert rapidly, so that nuclear motion remains the slowest process of interest; alternatively, one would require separate friction tensors (one for up spin, and one for down spin) as in the present letter.

\section{Conclusions and Outlook}\label{sec:conclusions}
We have demonstrated that a large Lorentz force can operate on nuclei  \textit{in equilibrium} for systems with \textit{complex-valued} Hamiltonians. For a simple model of  two shifted parabolas, with spin-orbit coupling, according to an analytic expression for the friction tensor, the magnitudes of the relevant frictional components ($\gamma_{\mu\nu}^{\mathrm{S}}$ and $\gamma_{\mu\nu}^{\mathrm{A}}$) can be controlled by tuning the driving force $\Delta$ and the inverse temperature $\beta$. The antisymmetric part can be one order larger than the symmetric part for low temperatures. Moreover, $\gamma_{\mu\nu}^{\mathrm{A}}$ and $\gamma_{\mu\nu}^{\mathrm{S}}$ can be of comparable
magnitude even when the phase change of the off-diagonal coupling is very small. All of these results show that,
 for any relaxation processes with an external magnetic field or/and spin-orbit coupling, careful consideration of a Lorentz force due to the nuclear Berry curvature is necessary. We have also provided \textit{ab initio} calculations of a diphenylmethane junction, showing the same conclusions as above.

Looking forward, one can imagine two scenarios whereby the antisymmetric nature of $\gamma_{\mu\nu}$ will be paramount. First, if one scatters a molecule off a surface in the presence of spin-orbit coupling
, there is the real possibility that the presence of $\gamma_{\mu\nu}^{\mathrm{A}}$ will contribute meaningfully to a spin-polarized chemicurrent. Second, there is a deep question about whether the Lorentz force described here can help explain spin-selectivity as found in chiral-induced spin selectivity (CISS) experiments\cite{naaman:2011:science:ciss_dna,naaman:2019:natrev,zollner2020insight}. In other words, if nuclear wave packets attached to different spins feel different forces, might not one consequence of such a difference be spin-polarized of a current through a system where nuclei and electrons interact? Such a claim might be verified experimentally by the presence of an isotopic CISS effect.
Finally, from a theoretical point of view, note that a recent
 paper has argued empirically that, for a molecule in the gas phase,  the Lorentz force is accentuated
dynamically when the molecule passes near a conical intersection that
is slightly modified by spin-orbit coupling\cite{wu2021electronic}.
For our part, we find a similar result near a metal surface, i.e. the effect of the Lorentz force is maximized
if $\hat{H}_\mathrm{s}$ admits an energy gap rather than displaying a true conical intersection.
In fact, according to Eq. (\ref{eq:ft_tls_antisym}), the antisymmetric part of the  friction tensor is zero
if one considers a gapless two-dimensional linear vibronic complex-valued Hamiltonian (See SM \ref{si:ci})\cite{ci_3d_note}.

Finally, in this letter we have analyzed the antisymmetric friction tensor that appears at equilibrium (with spin-orbit coupling). At the same time, a set of recent calculations has shown that a Berry force also appears when a molecule is placed between two leads out of equilibrium (without spin-orbit coupling)\cite{lu2010blowing,bode2012current}. To that end, the question remains as to what is the relationship between the equilibrium Lorentz force
analyzed here (derived in the case of a complex-valued Hamiltonian) and the previously published nonequilibrium Lorentz forces (derived in the case of real-valued Hamiltonian)\cite{dundas:2012:prb_berry,bode2012current}.  One can ask: Can the two Lorentz forces add to each other constructively? Can the forces be controlled individually by the properties of two leads? The present approach opens up the door to merge spintronics and nonadiabatic dynamics for an accurate description of spin-dependent current induced forces.

redpajama_set_name: RedPajamaArXiv


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text:
Kendall Newson (born March 5, 1980) is a former American football wide receiver in the National Football League. He was selected by the Jacksonville Jaguars in the 7th round (222nd overall) of the 2002 NFL Draft. He played collegiately at Middle Tennessee State University.

He was also a member of the Tennessee Titans, Miami Dolphins, Rhein Fire, and Hamilton Tiger-Cats

In 2013, he entered the world of pro fishing by competing in the Bassmaster Elite Series of tournaments.

References

1980 births
Living people
American football wide receivers
Middle Tennessee Blue Raiders football players
Jacksonville Jaguars players
Tennessee Titans players
Miami Dolphins players
Rhein Fire players
Hamilton Tiger-Cats players