264 – "The Return of Doctor Mysterio"
"The Return of Doctor Mysterio" is an episode of the British science fiction television series Doctor Who. First broadcast on BBC One on 25 December 2016, it is the twelfth Christmas special since the show's revival in 2005. It was written by Steven Moffat and directed by Ed Bazalgette. The episode received generally positive reviews from critics.
The episode stars Peter Capaldi as the Twelfth Doctor, and is the first to feature Nardole (Matt Lucas) as his companion, having been introduced in the previous episode "The Husbands of River Song". The episode is set in New York City, and involves the Doctor and Nardole linking with journalist Lucy Fletcher (Charity Wakefield) and a superhero called The Ghost (Justin Chatwin) to combat brain-swapping aliens.
In New York City on Christmas Eve of 1992, an 8-year-old boy named Grant wakes to find the Doctor dangling outside the window of his family's apartment and helps him come into his bedroom. Taking the boy to the rooftop, the Doctor reveals he accidentally set off a trap for a device he was building, and he enlists Grant to help complete it. However Grant mistakenly swallows a wish-granting gemstone needed for the device, believing it to be medicine, effectively being granted his wish to be a superhero. Abandoning the device, the Doctor makes Grant promise to not use his new superpowers before he leaves.
Returning to New York in 2016 with Nardole, whom he removed from Hydroflax's body and rebuilt, the Doctor investigates Harmony Shoals, a multinational research company. They encounter a news reporter, Lucy Fletcher, who is conducting a similar investigation. The group discovers that it is being secretly run by a group of living alien brains that transplant themselves into any living creature they need for their plans. They witness the killing of the company's owner, Mr Brock, for his body. Tracked down by Dr Sim, an employee the brains already took over, the group is suddenly rescued by a masked superhero named the Ghost, who afterwards transports Lucy close to her home. Returning to her apartment before her, the Ghost transforms back into Grant, who works for Lucy as a nanny. He is shocked to find the Doctor and Nardole waiting for him, having tracked him down via the gemstone fused inside his body.
When Lucy returns and sees the Time Lord, the Doctor reveals to her that the alien brains colonise planets by taking control of their prominent leaders, with Earth being their next target. Leaving Lucy to prepare for an interview with Grant's alter ego, the Doctor and Nardole track down the alien's ship in a low orbit and board it via the TARDIS. There, they discover that the ship's reactor is in a critical state and realise from Dr Sim that he intends to drop it on New York. Remembering an observation made by Nardole, the Doctor realises the city would be vaporised except for the Harmony Shoals building. World leaders would then take shelter in the company's other buildings within each capital city, believing Earth was under attack, effectively allowing the brains to take them over. After Dr Sim lets slip the ship is to be dropped at a designated time, the Doctor forces its descent ahead of schedule.
The costumes of Nardole, The Doctor, The Ghost and Lucy in this episode, on display at the Doctor Who Experience.
Ghost and Lucy are captured by the brains during the interview. They plan to transplant themselves into Ghost's body. Ghost flees to deprive the brains of their prize, then returns as Grant to protect Lucy. Unable to change the ship's course during its descent, the Doctor sends Grant a message requesting his help. Grant manages to stop the alien's ship from crashing into the city, but reveals himself as the Ghost to Lucy in the process. Lucy is won over and Grant takes her in tow as he disposes of the ship. The Doctor alerts UNIT, which shuts down Harmony Shoals, unaware that the alien brain in Dr Sims has escaped within one of their soldiers.
Back at Lucy's apartment, Grant informs the Doctor he will no longer use his powers and retire his costumed identity. As the Time Lord leaves, Lucy asks him why he is sad. The Doctor gives only a vague answer before departing. Nardole privately reveals that the Doctor is mourning the loss of River Song, but will ultimately recover. He leaves with the Doctor to assist him further.
At the beginning of the episode, the Doctor is constructing a device to reverse the paradoxes created during his previous visit in "The Angels Take Manhattan" (2012). The Doctor mentions that he usually gets "an invasion" every Christmas, a reference to the different invasions of Earth taking place during most Doctor Who Christmas specials.
The unnamed brain-swapping aliens last appeared in the 2015 Christmas special "The Husbands of River Song", where they were servants of King Hydroflax. Their main agent, Scratch, stated that they represented "the Shoal of the Winter Harmony."
The Doctor tells Lucy that he works for Scotland Yard, which he also did in "The Woman Who Lived" (2015). Previously, the Tenth Doctor told the guests at Lady Eddison's manor he was a chief inspector from Scotland Yard in "The Unicorn and the Wasp" (2008), while the Eleventh Doctor told President Richard Nixon he was an undercover operative from Scotland Yard (code-named "The Doctor") in "The Impossible Astronaut" (2011).
A cinema near Lucy's apartment features a film called The Mind of Evil, the name of a Third Doctor serial.
Nardole mentions that the Doctor cut him out of Hydroflax's body, referring to off-screen events following "The Husbands of River Song" where he was decapitated and his head was placed inside the artificially intelligent robotic body of King Hydroflax.
When the Doctor complains that Grant promised him never to use his powers, Nardole brings up the Time Lord policy of never interfering with other peoples or cultures, first mentioned in the Second Doctor serial The War Games (1969).
When clearing out the headquarters of Harmony Shoal, a UNIT officer prepares to contact Osgood, referring to Petronella Osgood who previously appeared in "The Day of the Doctor" (2013), "Death in Heaven" (2014) and "The Zygon Invasion" / "The Zygon Inversion" (2015).
Both the Doctor and Nardole refer to the final 24-year night the Doctor spent with River Song ("The Husbands of River Song") and her eventual death in the Library ("Forest of the Dead").
Superman's creators, Jerry Siegel and Joe Shuster, are referenced when Mr Brock directs the gathered reporters to ask further questions of "Miss Shuster and Ms. Siegel".
Grant has roughly the same standard powers of Superman, including flight, super-strength, super-speed, being bulletproof, and possessing X-ray vision, along with other unconventional powers. He gains his abilities from a stellar-powered object (a gemstone made from a star, in the episode), much as Superman gains his from Earth's yellow sun.
The Harmony Shoals building in New York featured in the episode has a large globe on top of it, making it resemble the Daily Planet building, a major setting of Superman stories.
Grant prefers being called "mild-mannered", as Superman's alter ego is often characterized. He also follows the same moral code as Superman when operating as the Ghost, and transforms in a similar fashion by tearing open his shirt to reveal his superhero costume underneath.
The special features a number of elements that mimic those from Richard Donner's Superman: The Movie. One scene involves the Ghost voicing his hope that Lucy's close call at Harmony Shoal hasn't put her off journalism, paralleling the same scene in the film in which Superman hopes Lois is not put off from flying after he rescues her from falling out of a helicopter. Lucy also conducts a rooftop interview with the Ghost reminiscent of Lois' interview with Superman in the film.
Lucy Fletcher is named after Lois Lane's sister Lucy. Her character is similar to Lois' in that she does not realize that her old high school friend and current nanny is the superhero Ghost. The initials "L.L." used by several characters of the Superman comics (including Lois Lane, Lana Lang, Lex Luthor, Linda Lee, Lori Lemaris, Letitia Lerner, Lena Luthor and Lyla Lerrol) is used in Lucy's married name: Lucy Lombard.
Several characters from Marvel Comics decorate the walls of young Grant's bedroom. The Doctor questions Spider-Man's unusual origin of being bitten by a radioactive spider; he opines that radiation poisoning would be the likely result. A "Joe's Pizza" is shown within the city, which is where Peter Parker worked briefly in the movie Spider-Man 2. The Doctor counsels Grant that "with great power comes great responsibility," an adage associated with Spider-Man.
Batman is briefly referenced after the Ghost drops Lucy off at her apartment building. When the baby monitor he is carrying goes off, Lucy mistakes it for a signal device and asks if the Bat-Signal is now an app.
The Doctor uses the augmented reality game app Pokémon Go to create a distraction at Harmony Shoal's Tokyo headquarters.
The episode was revealed and the first trailer was shown at the 2016 New York Comic Con on 7 October 2016. A preview clip was shown as part of the Children in Need broadcast on 18 November 2016.
The episode received cinema screenings in Australia and New Zealand on 26 December 2016, in Canada on 26 and 28 December 2016, and in the United States on 27 and 29 December 2016.
The episode had an official rating of 7.83 million viewers in the UK with a 31.2% share, making it the 6th most watched show on Christmas Day 2016. The overnight rating was 5.68 million, a share of 27.1% of the total TV audience. The episode received an Appreciation Index score of 82. It also received 1.7 million viewers on BBCA, was BBC America's top telecast of the year across all key demographics, and was the most talked about Christmas Day television programme on Facebook and Twitter.
The episode received generally positive reviews from critics. It holds a score of 89% on Rotten Tomatoes based on 18 reviews, with an average score of 7.89. The site's consensus reads "The Return of Doctor Mysterio is a welcome return of Doctor Who after a year's absence, with the added fun of seeing Steven Moffat take a heroic swing at his version of a Superman story."
The Daily Telegraph gave a positive review of five out of five stars and summarized that the episode was "a romp with a classic feel and cross-generational appeal". Andrew Billen writing in The Times gave the programme four stars out of a possible five. Billen said that Capaldi was at his warmest and that Nardole (Matt Lucas) "added panto brio to an already exuberant episode". The Guardian gave a positive review of The Return of Doctor Mysterio saying "Capaldi takes Manhattan!" ... "Cosmic baddies are inserting alien brains into world leaders' heads in the Christmas special. It's timely, top-of-the-tree fun – and Peter Capaldi and Matt Lucas are a pantomime treat".
IGN said ""The Return of Doctor Mysterio" is a pretty lightweight entry in the Twelfth Doctor's oeuvre, which considering the events of last season isn't necessarily a bad thing. But the different elements of the episode don't come together as smoothly as they could, and the emotional through line for the Doctor is treated mostly as an afterthought" but gave it 7.0 out of 10. The A.V. Club gave a mixed review saying that "Doctor Who takes a jolly detour to superhero goofiness".
The episode was released on DVD and Blu-ray in the United Kingdom on 23 January 2017, with a U.S. release following on 21 February 2017.
^ a b c d e f g h i j "The Return of Doctor Mysterio Review – Doctor Who TV".
^ a b c d e "The Return of Doctor Mysterio, Doctor Who – The Return of Doctor Mysterio: The Fact File – BBC One".
^ a b "'Doctor Who' Christmas Special Recap: The Return of Doctor Mysterio". 26 December 2016.
^ a b "'Doctor Who': 10 Things You May Not Know About 'The Return of Doctor Mysterio' – BBC America".
^ a b "DOCTOR WHO Gives Christmas a POW in 'The Return of Doctor Mysterio' (Review) – Nerdist". 25 December 2016.
^ "The Return of Doctor Mysterio, Doctor Who – The Return of Doctor Mysterio: The Fact File – BBC One". bbc.co.uk. BBC. Retrieved 27 December 2016.
^ a b c d e f "Doctor Who Christmas special: The Return Of Doctor Mysterio nerdy spots & Easter eggs".
^ "Doctor Who Christmas Special: All The Comic Book Easter Eggs".
^ a b c Hogan, Michael. "Doctor Who, The Return of Doctor Mysterio review: the happiest, most heroic Christmas special in years". The Telegraph. Retrieved 26 December 2016.
^ Carter, Chris (28 December 2016). "Pokemon Go gets a quick off-screen cameo in Doctor Who". Destructoid. Retrieved 29 December 2016.
^ "Doctor Who Superhero Adventure for Christmas Day". Doctor Who. 7 October 2016. Retrieved 3 December 2016.
^ "The Return of Doctor Mysterio: The Sneak Peek!". Doctor Who. 21 November 2016. Retrieved 3 December 2016.
^ Foster, Chuck (22 November 2016). "The Return of Doctor Mysterio to be shown in Australian cinemas". Doctor Who News. Retrieved 3 December 2016.
^ Foster, Chuck (2 December 2016). "New Zealand cinema outing for The Return of Doctor My"sterio". Doctor Who News. Retrieved 3 December 2016.
^ Foster, Chuck (23 November 2016). "Canada added to Doctor Mysterio cinema outings". Doctor Who News. Retrieved 3 December 2016.
^ Foster, Chuck (17 November 2016). "The Return of Doctor Mysterio to air in US theatres". Doctor Who News. Retrieved 3 December 2016.
^ "The Return of Doctor Mysterio – Official Rating". Doctor Who News. 3 January 2017.
^ "The Return of Doctor Mysterio – Overnight Viewing Figures". Doctor Who News. 26 December 2016.
^ "Doctor Who Guide: The Return of Doctor Mysterio". doctorwhonews.net. Retrieved 30 December 2016.
^ Petski, Denise (30 December 2016). "'Doctor Who' Christmas Special Breaks BBC America Ratings Record".
^ a b c "Doctor Who: The Return of Doctor Mysterio (2016 Christmas Special)". Rotten Tomatoes. Retrieved 12 November 2018.
^ a b "Doctor Who takes a jolly detour to superhero goofiness". 25 December 2016.
^ Setchfield, Nick (25 December 2016). "Doctor Who Christmas Special review: "Charm, imagination, and wit: these are the show's superpowers"". SFX Magazine. Retrieved 5 November 2018.
^ Smedley, Rob (25 December 2016). "'Doctor Who' review: 'The Return of Doctor Mysterio' is joyous and action-packed". CultBox. Retrieved 5 November 2018.
^ a b Collura, Scott (25 December 2016). "Doctor Who: "The Return of Doctor Mysterio" Review".
^ Nguyen, Hanh (26 December 2016). "'Doctor Who' Christmas Special Review: River Song Isn't Forgotten in Heartwarming Retro Superhero Adventure (Spoilers)". IndieWire. Retrieved 10 October 2018.
^ "The Doctor (Finally) Returns to TV in the Serviceable "Doctor Mysterio"". PopMatters. 3 January 2017. Retrieved 10 October 2018.
^ Ruediger, Ross (26 December 2016). "Doctor Who Christmas Special Recap: Man of Feel". Vulture.com. Retrieved 5 November 2018.
^ Mulkern, Patrick (25 December 2016). "Doctor Who Christmas special review: "a beautifully packaged hour of uplifting escapism"". Radio Times. Retrieved 5 November 2018.
^ "Doctor Who: The Return Of Doctor Mysterio – Christmas Special review". SciFiNow. Retrieved 10 October 2018.
^ a b Billen, Andrew (26 December 2016). "Forget the Midwives, the Doctor was the real star". The Times (72103). p. 14. ISSN 0140-0460.
^ "Doctor Who Christmas Special 2016 Review | The Young Folks". www.theyoungfolks.com. Retrieved 10 October 2018.
^ Lawson, Mark (26 December 2016). "Doctor Who: The Return of Doctor Mysterio review – Capaldi takes Manhattan!" – via The Guardian.
^ "Doctor Who – The Return of Doctor Mysterio [DVD] ". Amazon. Retrieved 3 December 2016.
^ "Doctor Who DVD news: Announcement for The Return of Doctor Mysterio: 2016 Christmas Special - TVShowsOnDVD.com". Archived from the original on 11 December 2016.
"The Empty Child" / "The Doctor Dances"
"The Doctor, the Widow and the Wardrobe"
"Dark Water" / "Death in Heaven"
"The Husbands of River Song"
This page was last edited on 17 December 2018, at 20:02 (UTC).


I am a human being over eleven years old, and I live in the United States of America, which means that I think about my weight. I can't help it (despite my little peach-colored pill), and after a year of starting posts about this topic and never finishing them, I've decided, it's time.
As I've mentioned before, I have a general rule against sharing personal stories about weight, diets, or workout regimens. But like any good rule, I believe there are exceptions and I'm hoping that this entry is one of them.
Let's start with numbers since numbers are easy and since they likely quell some curiosity. This morning, I weighed 147 pounds. About eleven months ago, I weighed 20 pounds less than that and when I delivered Teddy, I weighed 53 pounds more. We good so far?
OK, now for some background to those numbers.
As a senior in high school, I was deeply loyal to my schoolwork and the sports that I played. I had a family, a best friend, a boyfriend, and a life that I loved. I ate frosting out of the container when I made a cake, batches of mozzarella sticks with Brianne, and countless slices of Papa Gino's pizza at team dinners. And I didn't feel guilty about any of it. I knew who I was in my small New England suburb and I was proud of that person. When I left for college, I felt excited, eager, and blessed.
When I arrived at Bowdoin, I still felt the same way. I missed my family but I wasn't ever really homesick. At the same time, something unexpected happened.
When the honeymoon of orientation was over, I started to feel lost; not lost so much in terms of what to do but lost in terms of how I valued myself while I was doing it.
In Canton, I had been an above-average basketball player, swimmer, and gymnast. At Bowdoin, I was way below average at the first two, and gymnastics didn't even exist. In Canton, I wandered from class to class with the smartest kids in the school, but at Bowdoin, I was surrounded by students (like Brian) who were the valedictorian of their high school class and I definitely hadn't earned that top spot. All of the sudden, I felt average, really average, and despite that now, average sounds wonderful, at the time, I hated that feeling. It felt boring and empty; snobby and insecure; complex, and yet so very simple.
A very ironic thing added to my pain – before I left for college, I got my hair cut short, basically to the hairdo that I (unintentionally) have now. At the time I sat in my hairdresser's chair in August 1998, I wanted something new and different, but as soon as I got to Bowdoin and realized that I was new and my haircut was different, I regretted that decision. To be honest, I didn't regret it in any conscious way; I never stared in the mirror and thought to myself, I wish my hair were long again. But I just didn't feel right with short hair and deep down, I hoped that when it grew back, I'd be confident and happy again.
In search of that confidence and that happiness that I had somehow lost, I started to exercise. A lot. No matter the time of day or the weather or how much my knees hurt, I ran, swam, cross country skied, or stepped up and down on the StairMaster. Today, that all sounds fun (except maybe the StairMaster part) but it wasn't fun at the time. It was absolutely exhausting -- both for my body and for my mind. Unfortunately, however, I had no idea how to get either of them to rest. My mind had become a calculator for calories consumed and calories burned and despite that it was constantly doing math, no one ever knew.
In all honesty, my obsession with my weight wasn't about what other people thought. In fact, it wasn't even really about the number on a scale, either, and I rarely, if ever, weighed myself. My anxiety was really about what I thought about how I looked, how I felt in a new place, what I could (or could not) control.
Looking back on this poem is similar to looking back on August 8th of last year – it's like watching a thunderstorm storm in the distance after it's passed...oddly enough, it looks sort of beautiful...maybe mostly because it's passed.
Gradually, for several reasons, I grew out of obsessing about my weight. It wasn't so much that I solved the problem directly, but rather, that I found things that took priority over it -- Brian, my teaching job, law school, my kids. Over the years, I found peace with something that had previously tortured me and I was proud of that.
If you'd have asked me on August 7, 2012 about my feelings on my weight, I would have told you that I was satisfied with it. But deep down, I'd have been pleased to lose 10 or 15 pounds...a few from those extra handles above my hips, a few more from my C-section pouch, some from the flabbiness under my arms, and a bit from my inner thighs. Then, I'd feel great.
It turns out that there's a really quick way for me to lose 10 pounds, or hell, to lose 20...a cancer diagnosis. Despite that I'm that rare person who can eat meals through a bout of the flu, on August 8, 2012, I lost my appetite and I lost it bad.
I was literally so nauseous with worry that the thought of most foods made me want to throw up. It didn't help that most calls from the doctors with additional news on my diagnosis came around dinner time, and after those, sitting up straight felt like a chore, and scooping food into my mouth felt damn near impossible.
I didn't notice the weight loss at first; it was the least of my worries. But soon, I became concerned. I weighed myself and saw that I had lost ten pounds. I thought the cancer had started to kill me.
So I started to change the food that I was able to eat. While that deadly tumor was still in me, I decided to eat only the healthiest foods and pray that they would do everything possible to stop a single cancer cell from escaping from my breast. My life became mustard instead of mayo and cauliflower instead of ice cream. It wasn't painful, but rather, something that I could control amidst a storm of things that I couldn't.
Prior to my double mastectomy, I was generally frightened to exercise so I really didn't. Crazily (and with absolutely zero supporting science), I thought that exercise could propel a cancer cell from the invasive tumor and nothing was worth that.
It turns out, however, that even without exercise, eating healthy foods really does cause weight loss because I continued to drop; five, seven, ten more pounds. Despite that I had some control that I craved, I was terrified that I was withering away. Sadly, the madness of Hollywood helped me, as I distinctly remember telling myself, Angelina Jolie is alive and she's way thinner than me. But still, I knew that I was not built to look like Angelina Jolie or to look the way that I looked. I was supposed to be bigger than that, healthier than that.
At one point just before chemo, I met with a nutritionist at Dana-Farber. She was lovely and she gave me some useful information. But the most important thing that I took away from our meeting was that she would help me if eating continued to be such a challenge. There are ways we can get you to gain weight even if you're having trouble eating, she told me. I felt some peace.
In the end, as my worry about dying from cancer (and the related nausea) receded, my appetite returned. I'd guess that today I weigh exactly what I weighed on August 8th of last year. And if you want to know what I think about my weight right now...what I really feel about it...I feel great.
I'm still human, still over eleven years old, and still living in the U.S.A., so obviously, I still think about my weight. But now, I think about it so, so much less. When I do, I have pretty healthy thoughts and I really, really appreciate them.
This change in me is not, however, all because of cancer (or because of writing). I had grown far away from the girl who wrote that poem long before cancer. Still, some tiny parts of her toxicity lingered in me. Maybe while the chemo worked on any cancer that remained in my system, it also wiped out any of that girl's toxic leftovers because I honestly don't feel it anymore. Here's what I do feel.
I feel like I have finally learned what my body is supposed to look like when it's in a healthy state. I'm supposed to have some extra handles above my hips, some flabbiness under my arms, and inner thighs that remain untoned. These aren't things I should fight against or wish away. They're how things are supposed to be, maybe not for Angelina Jolie or for Victoria's Secret models, but for me.
I recently read an article in the newspaper about some number of teenage (and even pre-teen) girls who are taking pictures of their inner thighs and sharing them through social media. The most desired photos are sent by one who is thin enough that her inner thighs don't touch when she stands with her legs together. It makes me sick to think that girls are doing this, worrying about this, trying to change something that's not supposed to be changed.
I also know that there's not much that someone can say to help a person who is battling weight issues. Yes, I think a good therapist could be key, but a family member, friend, or blogger is probably not going to make much of a lasting difference. The process of learning to value, care for, and protect the body we were given is a long and complicated one.
Nevertheless, I want to assert my wishes for my own kids. I hope that they enjoy frosting out of the container when they make a cake, batches of mozzarella sticks with their best friends, and countless slices of Papa Gino's pizza at their team dinners. I hope they learn, as soon as possible, what their body is supposed to look like when it's healthy and I hope that they never do anything to try to change that shape. I hope they exercise and generally eat well because it feels good and because it will make them stronger. I hope they look in the mirror and see a person they are proud of (but not too proud of), and that they don't just see hips, arms, or inner thighs.
Finally, I hope, so very deeply, that my kids know that I believe they are the most beautiful people in the world. Because I really do. Whatever their weight.


text:
Biografia
Bičurin proveniva da una famiglia di Ciuvasci, il padre era prete ortodosso. Studiò presso il seminario di Kazan'. Fu inviato a Pechino alla testa di una missione russa e vi rimase per 17 anni. I suoi interessi erano orientati alla storia della Cina ed alla lingua cinese. Accusato dai suoi superiori di scarso zelo religioso, gli venne tolto il rango di abate e fu rinchiuso nel monastero di Valaam. Qui tradusse una gran quantità di manoscritti cinesi antichi e medievali, che fino ad allora erano sconosciuti in Europa. Successivamente egli pubblicò una serie di scritti su Cina, Mongolia, Tibet, ecc., in gran parte di fonte cinese, e sulla storia della Mongolia, la geografia, religione, statistiche e agricoltura.

Nel 1835 gli venne conferito il premio Demidoff. Nel 1837 egli aprì la prima scuola di lingua cinese dell'Impero russo.

Per i suoi contributi alla sinologia, fu nominato membro delle Accademie delle scienze di Russia, di Prussia e di Francia.

Opere

 Osservazioni sulla Mongolia (San Pietroburgo 1828)
 Descrizione del Tibet (San Pietroburgo 1828)
 Descrizione della Zungaria e del Turkistan orientale (San Pietroburgo 1829, 3 Bde.)
 Cina, i suoi abitanti, tradizioni, usanze e chiarimenti (San Pietroburgo 1840)
 Descrizione statistica della Cina (San Pietroburgo 1841)
 Grammatica della lingua cinese (San Pietroburgo 1838)
 Dizionario cinese-russo
 Storia dei Mancesi fino al loro ingresso in Cina (in collaborazione con un altro membro della Missione in Cina, Leontjewski)
 Descrizione dei regni cinesi dell'ovest (scritto con l'archimandrita Daniel Sybillow)

Note

Altri progetti

Collegamenti esterni
  Bitschurin in Meyers Konversations-Lexikon, 4. Auflage. Band 2, Verlag des Bibliographischen Instituts, Leipzig/Wien 1885–1892, S. 989.
  Biografia

redpajama_set_name: RedPajamaWikipedia


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text:
What's All The Hype About Rafale? It's Deadly Specifications Will Show You
FactsIndian Air Force
By Aritra Banerjee
What is so great about Rafale
Following over a year of controversy and political slugfests, the first of the 36 uber-sophisticated Dassault Aviation designed, Rafale fighter jets have been inducted into the Indian Air Force's deadly arsenal. The country's Defence Minister Rajnath Singh has personally received the much-awaited French fighter aircraft, during his visit to France. Speaking about the Induction of the Rafale Fighter jet, the Defence Minister said, "This is a new milestone in bilateral ties." The first batch consisting of four Rafale fighter jets will make its way to India by May 2020, significantly bolstering the IAF's offensive capabilities. But what is the hype about the French-built aircraft? How will it enhance India's aerial superiority? To understand that, we must look at the tale of the tape.
Indian Defence Minister Rajnath Singh in France checking out the Rafale
The Tale Of The Tape
The Rafale fighter jet in all its glory!
1.) Delta Wings Enhance The Rafale's Stability
The Rafale is both an aeronautical and technological masterpiece! It's ultra-modern combat features give a new definition to the phrase 'death from above.' The Dassault Rafale Multi-Role fighter comes designed with delta wings; this uniquely aerodynamic feature keeps the french fighter aircraft uniquely stable while cruising at supersonic speeds!
2.) Unique Engine Design
The Rafale's unique engine design aids the throttle, seamlessly transitioning from combat to idle to combat power in a span of fewer than three seconds!
3.) Can Covertly Detect Targets
The Rafale fighter jet is immune to Radar jamming furthermore the Dassault Aviation designed aircraft has the capability to clandestinely detect multiple targets at sea, air and land.
4.) Real-Time 3D Mapping of The Topography
The Rafale Fighter jet possesses state of the art early detection and tracking capabilities, as aforementioned. This allows the pilot to monitor multiple targets and generate real-time three-dimensional maps of the terrain the aircraft is soaring over.
5.) Speed and Altitude
The Dassault Rafale has a top speed of 1.8 mach, meaning the fighter jet can cover an average distance of 2,222.6 kilometres per hour. The deadly aircraft can climb up to altitudes of 50,000 feet with relative ease. The Rafale can fly for approximately 3,700 kilometres before having to refuel. The aerial longevity of the aircraft can be increased through mid-air refuelling.
6.) Unparalleled Payload Capacity
The Rafale is absolutely beyond any comparison when it comes to its munitions/ordnance and overall payload capacity. The fighter jet has the capability of carrying over 9,500 kilograms of explosives and other munitions. That is significantly more than any of the IAF's other aircraft, with the Sukhoi 30 MKI coming at a distant second with a capacity of 8,000 kilograms.
Indian Air Force 2020
The IAF's once renowned and recently defunct Golden Arrows squadron has been revived to fly the Rafale
The strategic edge, which the Induction of the Rafales will give India cannot be stressed enough and with the scheduled induction of the first batch next year, India's Air Warriors will have a busy time rigorously training the new aircraft system. It is safe to say that by 2020, the country will have a new squadron of highly trained pilots on this beast of a machine and will further cement India's image as a military power!
Dassault Rafale
Aritra Banerjeehttps://www.ssbcrack.com/
Defence Correspondent at SSBCrack.
TES 49 Cut Off Marks Out Now
Maroon Beret Ceremonial Parade 14 January 2023
Fake Indian Air Force Posing as a Wing Commander Caught
Indian Navy's MiG 29K Crashed in Goa
Difference Between Indian Air Force Old Uniform vs New Combat Uniform
All About New Weapon Systems (WS) Branch of Indian Air Force
Indian Army Helicopter Crashed, Lost One Pilot
SSBCrack - October 5, 2022
Flight Lieutenant Tejaswi Ranga Rao First Woman Wizzo of IAF SU-30 MKI Fleet
6 IAF Officers Charged with Murder after Air Force Cadet Found Dead
Meet Indian Air Force First Women Chinook Pilots
General Manoj Pande flew an IAF Apache attack helicopter over the Ladakh region
Like Father, Like Son: IAF Chief Flew a Sortie with Son
What is Exercise Pitch Black 2022
All About Helicopter Training School (HTS) and How To Join It
Mausami Sharma - September 6, 2022
Garud Commandos Maroon Beret Ceremonial Parade 03 Sep 2022
What makes AWACS different from AEW&C?
Siddhant Sandhu - August 29, 2022
IAF fires 3 officers for launching a missile inadvertently into Pakistan
Difference between IAF Sukhoi 30 vs IAF Rafale
Mausami Sharma - August 8, 2022
Sisters tied Rakhi to Wing Commander Mohit Rana
Nation remembers braveheart Flt Lt Advitiya Bal

redpajama_set_name: RedPajamaCommonCrawl


text:
Salt 'n' Pepa brandishing thir favorite bread
1,000 Jewish kids want to break a Guinness World Record – using challah
Jewish kids, moms and celebrities – including Salt 'n' Pepa – are teaming up to try and break the Guinness World Record for the biggest baking session in the world. The goal: 'Jewish unity.'
Itamar Eichner|Published: 01.12.16 , 23:23
What do Salt 'n' Pepa, Ian Ziering and Elon Gold have in common? They're all joining forces in order to try and break a Guinness World Record, along with a number of other celebrities.
They'll be joined by at least 1,000 Jewish kids on Tuesday in an attempt to break the record for the biggest number of people to take part in a baking session.
Celebrities are teaming up with Jewish kids and moms to bake challah en masse
שליחה לחבר
כתובת דוא''ל של החבר שמך כתובת הדוא''ל שלך נושא
הקלידו את הקוד המוצג
תמונה חדשה
הסרטון נשלח לחברך
הטמעת הסרטון באתר שלך
קוד להטמעה:
The attempt is the initiative of a number of Jewish moms in New York – religious and secular – and will also include non-Jewish moms. The mammoth baking event is to take place at New York's famous Hilton hotel.
Officially, the kids are competing in the category of "biggest baking lesson in the world," but they are actually trying to bake challahs in the largest number ever, and have invited representatives from the Guinness Book of Records to the event in order to supervise it and confirm that the record has been broken.
"We have so far registered over 700 children, 350 parents and 50 volunteers – and the number of children is growing all the time," said Bryce Gruber, a Jewish journalist and one of the organizers of the contest.
"We want to reach 1,000 children. It will be a record-breaking evening – something that these boys and girls will remember all their lives."
The moms behind the contest come from all walks of life. "It's great to see communities finding a common denominator," Gruber added. The goal, according to the contest's initiators, is "to advance Jewish unity."
The children participating in the competition are aged between five and 13.
"There is something very special and unifying about so many Jews from different backgrounds meeting and doing a mitzvah," said Gili, the mother of one of the participants and one of the event's organizers.
"I love Shabbat, and there's nothing more fun on Shabbat than challah," announced comedian Elon Gold, who called on children "to prepare the best challah in the world."


Earlier this week, Banipal sent out details of their 43rd issue, which will be a celebration of pioneer translator Denys Johnson-Davies.
Davies, who Edward Said once called "the leading Arabic-English translator of our time," has translated more than twenty-five volumes of short stories, novels, plays, and poetry, in addition to writing a number of children's books, a memoir, and several works of fiction.
The issue will also feature a number of works of fiction and poetry, including excerpts of the six novels shortlisted for the International Prize for Arabic Fiction and "guest literature" from Korea.
Other scheduled issues include Banipal 44, with a focus on "Women Novelists," set for release in the summer of 2012 and Banipal 45:Writing Palestine, which is scheduled for publication in the fall.
An extract of his translation of Hunger, by Mohamed al-Bisatie.
Translations of Mahmoud Darwish poems.
An excerpt of Johnson-Davies' memoir, Memories in Translation.
"House of Flesh," Yusuf Idris.


text:
Andrei Jewgenjewitsch Iwaschin (; * 30. Juni 1999 in Armawir) ist ein russischer Fußballspieler.

Karriere

Verein
Iwaschin begann seine Karriere beim FK Krasnodar. Zur Saison 2017/18 rückte er in den Kader der drittklassigen Zweitmannschaft Krasnodars. Für Krasnodar-2 kam er in jener Spielzeit zu sechs Einsätzen in der Perwenstwo PFL. Zu Saisonende stieg das Team in die Perwenstwo FNL auf. Sein Debüt in der zweithöchsten Spielklasse gab er im Juli 2018 gegen den FK Sibir Nowosibirsk.

In der Saison 2018/19 absolvierte der Außenverteidiger 30 Zweitligaspiele für Krasnodar-2, zudem kam er für die nun drittklassige Drittmannschaft ebenfalls viermal zum Einsatz. Im März 2020 stand Iwaschin gegen den FK Ufa erstmals im Kader der ersten Mannschaft Krasnodars. In der Saison 2019/20 absolvierte er 25 Zweitligapartien und eine für Krasnodar-3.

Nationalmannschaft
Iwaschin spielte zwischen 2014 und 2015 für die russischen U-15- und U-16-Auswahlen.

Weblinks

Fußballspieler (FK Krasnodar)
Russe
Geboren 1999
Mann


The population density in Downtown is 18% lower than Jersey City.
The median age in Downtown is 4% higher than Jersey City.
In Downtown 55.57% of the population is White.
In Downtown 8.84% of the population is Black or African American.
In Downtown 27.70% of the population is Asian.
In Downtown, 28.1% of people are of Hispanic or Latino origin.
Source: The Downtown, Jersey City, NJ demographics data displayed above is derived from the 2016 United States Census Bureau American Community Survey (ACS).


Well !! they came,left.. yet they never did so, they mentally enslaved us and continue to entrap us. We wake up from the coma, get small fits, look at one two issues now and then and slumber off again. The Indian public continues to suffer from colonial laws,which are not just irrelevant but in some ways against basic principles of human rights.
2.Our Mai baap culture is continues to prevail. Why do we not have better ways of taking in talent in the government services.Students slog for an exam and based on rank we provide them postings, take foreign services for e.g, How have we ensured the domain expertise needed for international relations in the exam, I could take Pali and Hindi literature and be a diplomat. This is crazy and provides some reasons for lot things that have gone wrong for India internationally, those are better left unsaid. Is it not time to have a seperate exam for such services which actually take in your interest to serve as a diplomat or a public administrator like the U.S does. How do we really have the depth to focus on international affairs ? When we take up roles for India in such specialised fora is it the passion, the domain knowledge or just the hard work of years for the exam that should matter?
3. Why do we still have the Railway budget? When 70% of the country is based on agriculture Why not have a agricilture budget? When britishers had this their priorities were clear, they focussed on the loot and railways development formed the backbone of the loot infrastructure.
4. For 53 years after independence until 2000 we presented the budget at 5:00 pm Why because we wanted the Britishers to hear them, and pass it at their noon time.Well even in 1999 thats completely nuts, how could we do that.We forgot, did not realise it, followed traditions?? It took 53 years to understand.
5. The Indian Flag is another case. A lot of us have not really hoisted Indian flags at our homes why? Because we were told it was inappropriate by law. What a crappy law. Imagine how good it might have been if we could really do so in our childhood. Luckily today we have better laws,we are allowed to, but it was not granted it took individuals to struggle to get this done.
These are just few examples, some of them came up during my discussions with Kumara Guru who in Boston today, I am sure there are tons more. Why don't we look at all of them for once and set out for better laws that actually uphold liberty, equality and fraternity in our way and really bury our past. They are gone, isn't it really time to bury their laws for once and all.
After a long time !!


text:
//
//  GDataFeedSpreadsheetList.m
//

#import "GDataEntrySpreadsheetList.h"
#import "GDataEntrySpreadsheet.h"
#import "GDataFeedSpreadsheetList.h"
#import "GDataCategory.h"

@implementation GDataFeedSpreadsheetList

+ (GDataFeedSpreadsheetList *)spreadsheetListFeedWithXMLData:(NSData *)data {
  return [[[self alloc] initWithData:data] autorelease];
}

+ (GDataFeedSpreadsheetList *)spreadsheetListFeed {
  GDataFeedSpreadsheetList *feed = [[[self alloc] init] autorelease];
  [feed setNamespaces:[GDataEntrySpreadsheet spreadsheetNamespaces]];
  return feed;
}

#pragma mark -

+ (void)load {
  [GDataObject registerFeedClass:[self class]
           forCategoryWithScheme:nil
                            term:kGDataCategorySpreadsheetList];
}

- (id)init {
  self = [super init];
  if (self) {
    [self addCategory:[GDataCategory categoryWithScheme:kGDataCategorySchemeSpreadsheet
                                                   term:kGDataCategorySpreadsheetList]];
  }
  return self;
}

- (Class)classForEntries {
  return [GDataEntrySpreadsheetList class];
}

@end

redpajama_set_name: RedPajamaGithub


From Arenal to Mal Pais we have Collective Shared Shuttles, Private Services.
Shared Collective Shuttles have 1 departure per day, in the morning Arenal to Mal Pais. This service takes 7 hrs from Arenal to Mal Pais.


text:
NEWS HOME » INDIA
Arunachal Pradesh: Senior Congress leader from Tawang Thupten Tempa passes away
Itanagar (Arunachal Pradesh) | October 8, 2022 4:59:06 AM IST
Former State Minister and senior Congress leader from Tawang, Thupten Tempa passed away at Ramakrishna Mission Hospital in Itanagar on October 7 evening.
Chief Minister Pema Khandu tweeted, "Saddened by passing away of Tempa Ji... May Lord Buddha provide peace to his soul..."
Earlier on Thursday, the Congress leader complained of abdomen pain and was hospitalized on Friday evening. Tempa's condition worsened due to low blood pressure.
Tempa worked as a bureaucrat before joining active politics. He studied MA in International Relations and M.Phil in Diplomacy from JNU, New Delhi.
In 2019, Tempa unsuccessfully contested an INC ticket from 2-Tawang Assembly Constituency against BJP's Tsering Tashi.
Deputy Chief Minister Chowna Mein expressed his condolences on his demise and said, "Deeply saddened to learn of the passing away of a senior leader of our State and former Minister, Shri Thupten Tempa ji. His contributions to the development of our State shall always be remembered. My thoughts & prayers are with his family and well-wishers at this hour. My Heartfelt condolences! May his soul rest in eternal peace."
While, MP Tapir Gao tweeted, " I am really saddened to hear about the passing away of Shri Thupten Tempa ji, a very senior leader of our state. I pray Lord Buddha gives strength to the bereaved family to overcome the loss at this time and also offer my deepest condolences. May his Soul Rest in Peace.
State BJP president, Biyuram Wahge said " I am deeply shocked to know about the sudden demise of our veteran leader Shri Thupten Tempa ji. My deepest condolences go to the bereaved family in this hour of grief. May his soul rest in peace. (ANI)


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Any violations in this respect will be prosecuted under civil and criminal law.
German law shall be exclusively applicable.


text:
\section{Introduction}
\label{sec:introduction}
The parametric dependence of an eigenvector of an operator
often exhibits anholonomy in its phase
~\cite{GeometricPhaseReview}.
A simple demonstration of the phase anholonomy in an eigenvector
of a Hamiltonian is shown by Berry~\cite{Berry:PRSLA-430-405}:
Prepare the system to be in an eigenstate of
the Hamiltonian, whose energy spectrum is assumed to be discrete and
nondegenerate.
During the adiabatic change of the parameters of the Hamiltonian,
which is kept to be nondegenerate along the change,
the system continuously remains to be in an
eigenstate of the instantaneous Hamiltonian, according to
the adiabatic theorem~\cite{Born:ZP-51-165}.
When the parameter returns to its initial value,
after the adiabatic change along a closed path in the parameter space,
the difference between the initial and the final state vectors is only
in its phase, which is composed by two ingredients: One is
called a dynamical phase that is determined by the accumulation of the
eigenenergy along the adiabatic time evolution. The other is called
a geometric phase, or the phase anholonomy that reflects
the geometric
structure of the family of eigenvectors in the parameter space.
There is a non-Abelian generalization of the phase anholonomy:
This was pointed out by Wilczek and Zee in the parametric change of an
eigenspace of a Hamiltonian that has a spectral degeneracy%
~\cite{Wilczek:PRL-52-2111}.
The phase anholonomy appears in various fields of physics, besides
quantum mechanics, and brings profound
consequences~\cite{GeometricPhaseReview}.

Recently, Cheon found exotic anholonomies, which are completely different
from the conventional phase anholonomy, in a family of systems with
generalized pointlike potentials~\cite{Cheon:PLA-248-285}.
Cheon's anholonomies appear, surprisingly, both in eigenenergies and
eigenvectors:
The trail of an eigenenergy along a change of parameters
on a closed path that encircles a singularity does not draw a closed curve
but, instead, a spiral.
Since the initial and the final eigenenergies in the closed path are
different eigenvalues of a Hermite operator,
the corresponding eigenvectors must be orthogonal.
Hence the eigenenergy anholonomy induces another anholonomy in the
direction of eigenvectors.
The origin of Cheon's anholonomies in the family of systems with the
generalized pointlike potentials
is identified with the geometrical structure of the family's
parameter space~\cite{Cheon:AP-294-1,Tsutsui:JMP-42-5687}.

In order to distinguish Cheon's anholonomy in the directions of eigenvectors
from
Wilczek-Zee's phase anholonomy, which
requires a degenerate spectrum and
transports an eigenvector into its nonorthogonal
direction in general along adiabatic changes on closed paths,
we will call the former an {\em eigenspace anholonomy\/}:
Wilczek-Zee's phase anholonomy concerns the change of an eigenvector within
a single and degenerate eigenspace and
Cheon's eigenspace anholonomy, which do not require spectral degeneracies,
concerns the journey of an eigenvector from one eigenspace
into another eigenspace.

We can easily expect that Cheon's anholonomies
would bring profound consequences in various fields of physics,
as is done by the phase anholonomy.
For example, in the adiabatic (sometimes referred to as
Born-Oppenheimer~\cite{Born:AP-84-457})
approximation~\cite{Born:1954},
it has been considered to be legitimate to assume that
an adiabatic potential surface, which is an eigenvalue of an electronic
Hamiltonian with a frozen nuclear configuration, is a single-valued
function of the nuclear configuration. The single-valuedness would
be broken if Cheon's eigenenergy anholonomy emerged. A similar question
may be raised in the Bloch theory in solid state physics~\cite{Kittel:ISSP}.
At the same time, Cheon's anholonomies may be applied to manipulate
quantum systems to transfer a quantum state adiabatically into
another state, as is suggested by Cheon~\cite{Cheon:PLA-248-285}.
The last point will be discussed more precisely in this paper.
However, all known examples of the eigenenergy anholonomy, up to now,
require an exotic connection condition
around a singular potential~\cite{Tsutui:JPA-36-275}.
Hence it is still worth to find systems that exhibit
Cheon's anholonomies.

The purpose of the present paper is to show Cheon's anholonomies
in periodically driven systems.
More precisely, we will discuss
quasienergy and eigenspace anholonomies with respect to Floquet operators
that describe unit time evolutions of the periodically driven systems.
First, we provide an instance of a quantum map, i.e., a quantum system
under a periodically pulsed perturbation~\cite{QuantumMap}.
The simplicity of the Floquet operators of quantum maps
allows us a thorough analysis.
In order to prepare it, the parametric dependence,
induced by the change of the strength of the perturbation,
of eigenvectors of the Floquet operators of quantum maps is reviewed in
Section~\ref{sec:adiabaticTransport}.
In Section~\ref{sec:rank1}, a quantum map that is perturbed by
a rank-$1$ operator is introduced.
The details of its properties are explained
in Appendices~\ref{sec:normalForm} and~\ref{sec:cyclicity}.
In Section~\ref{sec:existance}, it is
shown that the rank-$1$ perturbation, with respect to the original
Floquet operator, enables us to introduce a family of Floquet
operators to realize Cheon's anholonomies.
Several examples are shown in Section\ref{sec:examples}.
Second, the stability of the anholonomies is examined.
A geometrical analysis, which is shown in Section~\ref{sec:abundance},
of the family of Floquet operators
elucidates that the appearance of Cheon's anholonomies is not
restricted in the periodically pulsed systems and is also possible
in periodically driven systems in general.
Furthermore, we may claim that Cheon's anholonomies are abundant
in systems whose time evolutions are described by Floquet operators.
Among possible consequences and applications of our result,
Section~\ref{sec:manipulation} provides a discussion on a design
principle on quantum state manipulations along adiabatic passages.
Section~\ref{sec:summary} provides a discussion and a summary.
A part of the present result was briefly announced in Ref.~\cite{TM061}.

\section{Adiabatic transport of eigenvectors in a quantum map}
\label{sec:adiabaticTransport}

To prepare our analysis of quantum maps,
we review the parametric motions of eigenvectors and eigenvalues of
Floquet operators and the adiabatic theorem for periodically driven systems.
Let us consider a periodically pulsed driven system (with a period $T$)
described by the ``kicked'' Hamiltonian:
\begin{equation}
  \label{eq:kickedHamiltonian}
  \hat{H}(t) = \hat{H}_0 + \lambda\hat{V}\sum_{n\in\bbset{Z}}\delta(t - nT),
\end{equation}
where $\hat{H}_0$ and $\hat{V}$ describe
the ``free'' motion and the pulsed perturbation, respectively,
and $\lambda$ is the strength of the perturbation.
In the following, we focus on the stroboscopic description of the
state vector $\ket{\psi_n}$ at $t = nT-0$. The time evolution of
$\ket{\psi_n}$ is described by the quantum map
$\ket{\psi_{n+1}}=\hat{U}_{\lambda}\ket{\psi_{n}}$, where
\begin{equation}
  \label{eq:defUlambda}
  \hat{U}_{\lambda} = e^{-i \hat{H}_0 T/\hbar} e^{-i\lambda\hat{V}/\hbar}
\end{equation}
is a Floquet operator~\cite{QuantumMap}.
In the following, we set $\hbar = 1$.
In order to show a simple example of the parametric motions of
eigenvalues and eigenvectors, we assume that
the spectrum of $\hat{U}_{\lambda}$ contains only
discrete components and has no degeneracy.
At the same time, in order to avoid subtle issues that are
brought from the infinite dimensionality
of the Hilbert space $\mathcal{H}$~\cite{endnote:infinite},
we assume that $N\equiv\dim\mathcal{H}$ is finite.
This assumption does no harm to the descriptions of many systems
where an appropriate introduction of the truncation of the Hilbert space
is feasible.

Since $\hat{U}_{\lambda}$ (\ref{eq:defUlambda}) is unitary,
its eigenvalues $\{z_n(\lambda)\}_{n=0}^{N-1}$
are complex and on the unit circle, i.e., $|z_n(\lambda)|=1$.
The phase of $z_n(\lambda)$ indicates
the increment of the dynamical phase during the unit time evolution
whose initial state is the corresponding eigenstate $\ket{\xi_n(\lambda)}$.
The time-average of the dynamical phase
determines a quasienergy
$E_n(\lambda) =
- T^{-1} {\rm Im}[\ln z_n(\lambda)]
$
(or, $z_n(\lambda) = e^{-i E_n(\lambda) T}$).
Note that the value of quasienergy has an ambiguity because of the period
$2\pi/T$ in the quasienergy space.
We remark that the eigenvalue equation
\begin{equation}
  \label{eq:eigenvalueEq}
  \hat{U}_{\lambda} \ket{\xi_n(\lambda)}
  = z_n(\lambda) \ket{\xi_n(\lambda)}
\end{equation}
determines the eigenvalue and the eigenvector only pointwise
in $\lambda$.
By assuming the continuity about $\lambda$, we obtain the derivatives of
$E_n(\lambda)$ and $\ket{\xi_n(\lambda)}$~\cite{Nakamura:PRA-35-5294}:
\begin{eqnarray}
  \label{eq:leveldynamics}
  \pdfrac{}{\lambda} E_n(\lambda) &=&
  \frac{1}{T} \braOket{\xi_n(\lambda)}{\hat{V}}{\xi_n(\lambda)},
  \\
  \label{eq:vectordynamics}
  \pdfrac{}{\lambda} \ket{\xi_n(\lambda)} &=&
  -i A_n(\lambda)\ket{\xi_n(\lambda)}
  \nonumber \\ &&
  {}+ i\sum_{m\ne n}
  \frac{z_m(\lambda) \braOket{\xi_m(\lambda)}{\hat{V}}{\xi_n(\lambda)}}%
  {z_m(\lambda) - z_n(\lambda)}
  \ket{\xi_m(\lambda)},
  \nonumber\\
\end{eqnarray}
where $\ket{\xi_n(\lambda)}$ is assumed to be normalized and
$A_n(\lambda) \equiv
i \bra{\xi_n(\lambda)}\partial\ket{\xi_n(\lambda)}/\partial \lambda$
is a geometric gauge potential~\cite{Mead:JCP-70-2284}.
These derivatives compose a set of equations of motion for a
virtual time $\lambda$~\cite{endnote:leveldynamics}.
With a given ``initial condition'' of
$\{E_n(\lambda), \ket{\xi_n(\lambda)}\}_n$, at $\lambda = \lambda_0$,
we may integrate the equations of motion~(\ref{eq:leveldynamics}) and
(\ref{eq:vectordynamics}).
Note that, under the presence of
anholonomy~\cite{GeometricPhaseReview},
the single-valuedness of the solution
$\{E_n(\lambda), \ket{\xi_n(\lambda)}\}_n$ generally holds only locally
in the parameter space of $\lambda$.

The adiabatic theorem~\cite{Born:ZP-51-165}
for periodically driven systems~\cite{Holthaus:PRL-69-1596}
provides
a physical significance of the geometry (i.e., $\lambda$-dependence) of
$\ket{\xi_n(\lambda)}$.
Note that the parameter $\lambda$, which is supposed to be slowly changed,
is the strength of the perturbation that is applied periodically:
$\lambda$ will be changed from $\lambda_{\rm i}$ to $\lambda_{\rm f}$, during
the $M$ steps, where the corresponding time interval is $TM$.
Let $\lambda_j$ be the value of $\lambda$ at the $j$-th step
($0 \le j \le M$).
In particular $\lambda_0 = \lambda_{\rm i}$ and
$\lambda_{M} = \lambda_{\rm f}$.
The slowness of the change of the parameter is
expressed by the condition
$\lambda_{j+1} - \lambda_j = \mathcal{O}(M^{-1})$ as $M\to\infty$.
We start with an initial condition that, at $\lambda=\lambda_{\rm i}$,
the system is in an
eigenstate $\ket{\xi_n(\lambda_{\rm i})}$ of $\hat{U}_{\lambda_{\rm i}}$.
The final state $\ket{\Psi_{\rm f}}$ is
\begin{equation}
  \ket{\Psi_{\rm f}} \equiv
  \Torder\left[\prod_{j=1}^{M} \hat{U}_{\lambda_j}\right]
  \ket{\xi_n(\lambda_{\rm i})},
\end{equation}
where $\Torder$ represents a time-orderd (or, equivalently, path-orderd)
product.
According to the adiabatic theorem,
the final state will converge to
$\ket{\xi_n(\lambda_{\rm f})}$ as $M\to\infty$, except its phase.
In the following, we will evaluate the phase of the final state.
From the equation of motion~(\ref{eq:vectordynamics}), we have
\begin{equation}
  \begin{split}
    &\hat{U}_{\lambda} \ket{\xi_n(\lambda - \delta)}
    \\&=
    \exp\left\{-i E_n(\lambda)T + i A_n(\lambda)\delta\right\}
    \ket{\xi_n(\lambda)}
    \\ &\quad
    - \sum_{m\ne n}
    \frac{iz_m(\lambda)^2\bra{\xi_m(\lambda)}\hat{V}\ket{\xi_n(\lambda)}\delta}{z_m(\lambda) - z_n(\lambda)}\ket{\xi_m(\lambda)}
    +\mathcal{O}(\delta^2)
  \end{split}
\end{equation}
as $\delta\to0$.
According to the adiabatic theorem~\cite{Holthaus:PRL-69-1596},
we need only the first term above for the evaluation of the phase.
Hence we have
\begin{equation}
  \ket{\Psi_{\rm f}}
  \simeq
  \exp \left\{
    - i \sum_{j=1}^{M} E_n(\lambda_j) T
    + i \int_{\lambda_{\rm i}}^{\lambda_{\rm f}} A_n(\lambda) d\lambda

  \right\}
  \ket{\xi_n(\lambda_{\rm f})},
\end{equation}
as $M\to\infty$.
The first and the second terms in the phase factor correspond to the dynamical
and geometric phases, respectively~\cite{Berry:PRSLA-430-405}.

\section{Quantum map under a rank-$1$ perturbation}
\label{sec:rank1}

In order to demonstrate the simplest example of Cheon's
anholonomies in quantum maps, we employ a rank-$1$ perturbation
$\hat{V}=\ket{v}\bra{v}$ in Eq.~(\ref{eq:defUlambda})
with a normalized vector $\ket{v}$~\cite{Combescure:JSP-59-679}.
Since $\hat{V}$ satisfies $\hat{V}^2=\hat{V}$,
the quantum map~(\ref{eq:defUlambda}) has a periodicity about $\lambda$.
This is shown by an expansion of $\hat{U}_{\lambda}$ in $\hat{V}$,
\begin{equation}
  \label{eq:expandUlambda}
  \hat{U}_{\lambda} =
  \hat{U}_{0} \left\{1 - (1 - e^{-i\lambda}) \hat{V}\right\},
\end{equation}
which has  a $2\pi$ periodicity in $\lambda$.
Hence the parameter space of $\lambda$ is identified with a circle $S^1$.
We will discuss the parametric motion of quasienergies and
eigenvectors of $\hat{U}_{\lambda}$, along the changes of $\lambda$ on $S^1$.

Two kinds of ``trivial'' eigenvectors of $\hat{U}_{\lambda}$ are shown
in order to simplify the later analysis on Cheon's anholonomies.
For the first kind, we suppose that an eigenvector
$\ket{\xi}$ of $\hat{U}_{\lambda_0}$
is orthogonal to $\ket{v}$ and the corresponding eigenvalue is $z_0$.
Then, this implies that $\ket{\xi}$ is
also an eigenvector of $\hat{U}_{\lambda}$ for all $\lambda$
and the corresponding eigenvalue $z_0$ does not depend on $\lambda$.
In fact, we have
\begin{equation}
  \label{eq:orthoTriviall}
  \hat{U}_{\lambda}\ket{\xi}
  = \hat{U}_{\lambda_0}e^{-i(\lambda - \lambda_0)\hat{V}/\hbar}\ket{\xi}
  = \hat{U}_{\lambda_0}\ket{\xi}
  = z_0 \ket{\xi},
\end{equation}
where we used $\hat{V}\ket{\xi} =\ket{v}\bracket{v}{\xi}=0$
and $\hat{U}_{\lambda_0}\ket{\xi} = z_0 \ket{\xi}$.
In Appendix~\ref{sec:normalForm},
we will show that such trivial eigenvectors~(\ref{eq:orthoTriviall})
are created by a spectral degeneracy of $\hat{U}_{\lambda}$.
For the second kind, we suppose that $\ket{v}$ is an eigenvector
of $\hat{U}_{\lambda_0}$
and the corresponding eigenvalue is $z_0$.
If this is the case, all the eigenvectors of
$\hat{U}_{\lambda_0}$, except $\ket{v}$, are orthogonal to $\ket{v}$, and
accordingly become trivial eigenvectors of the first kind mentioned above.
Furthermore, $\ket{v}$ is also a trivial one in the sense that
$\ket{v}$ is an eigenvector of $\hat{U}_{\lambda}$ for all $\lambda$.
This is because
\begin{eqnarray}
  \label{eq:paraTriviall}
  \hat{U}_{\lambda}\ket{v}
  &=&
  \hat{U}_{\lambda_0}e^{-i(\lambda - \lambda_0)\hat{V}/\hbar}\ket{v}
  = \hat{U}_{\lambda_0} e^{-i(\lambda - \lambda_0)/\hbar}\ket{v}
  \nonumber \\
  &=&
  z_0 e^{-i(\lambda - \lambda_0)/\hbar} \ket{v},
\end{eqnarray}
where the corresponding eigenvalue
$z_0 e^{-i(\lambda - \lambda_0)/\hbar}$ depends on $\lambda$.
The analysis of the two kinds of trivial eigenvectors
are completed.

In the following, we assume the absence of these trivial eigenvectors
since they
are irrelevant to the later argument to look for Cheon's
anholonomies. A systematic procedure to reduce a Hilbert space
by excluding these trivial eigenvectors of $\hat{U}_{\lambda}$
is explained in Appendix~\ref{sec:normalForm}.
On the reduced Hilbert space $\mathcal{H}$, it is assured that the spectrum of
$\hat{U}_{\lambda}$ has no degeneracies for all $\lambda$.
In terms of $\hat{U}_0$ and $\ket{v}$,
this assumption turns out to be equivalent to the following two conditions.
(i) The spectrum of $\hat{U}_0$ is nondegenerate.
Note that we have already introduced another assumption that
the spectrum of $\hat{U}_0$ contains only discrete and
a finite number of components to assure the smoothness of the parametric
dependence of eigenvalues and eigenvectors on $\lambda$
in Section~\ref{sec:adiabaticTransport}.
(ii) $\ket{v}$ is not orthogonal to any eigenvector of $\hat{U}_0$,
otherwise the reduction is not complete.
Note that (ii) implies that $\ket{v}$ is not any eigenvector of $\hat{U}_0$.
Thus the conditions (i) and (ii) guarantee, for all $\lambda$,
\begin{equation}
  \label{eq:v_xi}
  0 \lvertneqq |\bracket{v}{\xi}| \lvertneqq 1
  \quad\text{for any eigenvector $\ket{\xi}$ of $\hat{U}_{\lambda}$},
\end{equation}
where either the lower or the upper bound of the equalities would hold
if any trivial eigenvector remains.

The conditions (i) and (ii) are further paraphrased with the help of
the notion {\em cyclicity}~\cite{RSICyclicity}, when we restrict
ourselves to
the dimensionality of the Hilbert space $\mathcal{H}$ being finite.
If $\hat{U}_0$ and $\ket{v}$ satisfy
$\mathcal{H} = \overline{{\rm span} \{(\hat{U}_0)^m \ket{v}\}_{m=0}^{\infty}}$%
~\cite{note:infiniteSpan},
$\ket{v}$ is called a cyclic vector for $\hat{U}_0$~\cite{RSICyclicity}.
It is shown in Appendix~\ref{sec:cyclicity}, the conditions (i) and (ii) are
equivalent to
(i') $\hat{U}_0$ has a cyclic vector
and (ii') $\ket{v}$ is a cyclic vector for $\hat{U}_0$,
respectively.
We will discuss the case that these assumptions are broken
in Section~\ref{sec:examples}.

\section{Cheon's anholonomies in quantum maps}
\label{sec:existance}

What happens to the quasienergies and the eigenvectors
when we adiabatically increase $\lambda$ by $2\pi$, the period of
the Floquet operator~(\ref{eq:expandUlambda}), and its spectrum,
starting from $\lambda=\lambda_0$?
The argument above suggests that we may have a conventional
(Abelian) phase anholonomy that appears only in the phase of
the eigenvectors.
However, the following argument will elucidate that we meet
Cheon's anholonomies in quasienergies as well as in eigenspaces.

First, we examine quasienergies $E_n(\lambda)$ ($0\le n <N = \dim\mathcal{H}$).
Note that we have $N$ cases to choose ``the ground quasienergy''
due to the periodicity in the quasienergy space.
Once we choose a ground state, whose quantum number is assigned to $0$,
the quantum number $n$ ($<N$) is assigned so
that $E_n(\lambda)$ increases as $n$ increases.
More precisely, in order to remove ambiguities due to the periodicity in
the quasienergies, we choose the branch of the quasienergies,
at $\lambda=\lambda_0$,
as $E_0(\lambda_0) < E_1(\lambda_0) < \cdots < E_{N-1}(\lambda_0)
< E_0(\lambda_0)+2\pi T^{-1}$ holds,
where $E_{0}(\lambda_0)$ and $E_0(\lambda_0)+2\pi T^{-1}$ correspond
to the same eigenvalue $z_0(\lambda_0) = e^{-i E_{0}(\lambda_0) T}$.
For brevity, we identify a quantum number $n$ with $n+N$.

To examine how much the ground quasienergy $E_0(\lambda_0)$ increases
during a cycle of $\lambda$, we evaluate
\begin{equation}
  \label{eq:DEnIE}
  \Delta E_n \equiv
  \int_{\lambda_0}^{\lambda_0+2\pi}
  \pdfrac{E_n(\lambda)}{\lambda} d\lambda.
\end{equation}
Note that $\Delta E_n$ is ``quantized''
due to the periodicity of the spectrum, e.g., we have
\begin{equation}
  \label{eq:quantizedDE0}
  \Delta E_0 =  E_{\nu}(\lambda_0) - E_0(\lambda_0) \mod 2\pi T^{-1}
  \quad\text{for some $\nu$},
\end{equation}
because $E_0(\lambda)$ should arrive at $E_{\nu}(\lambda_0)$
for some $\nu$ as $\lambda\nearrow \lambda_0+2\pi$.
To determine which $\nu$ is possible or not,
we evaluate the integral expression~(\ref{eq:DEnIE}) of $\Delta E_n$ with
$\partial {E_n(\lambda)}/\partial\lambda
= T^{-1} \braOket{\xi_n(\lambda)}{\hat{V}}{\xi_n(\lambda)}$~%
\cite{Nakamura:PRA-35-5294}.
Since $\hat{V}$ satisfies $\hat{V}^2=\hat{V}$,
the eigenvalues of $\hat{V}$ are only $0$ and $1$.
Accordingly we have
$0 \le \partial {E_n(\lambda)}/\partial\lambda \le T^{-1}$.
However, the equalities for the minimum and the maximum cannot hold
because of $ \partial{E_n(\lambda)}/\partial\lambda
= T^{-1} |\bracket{v}{\xi_n(\lambda)}|^2$
and
$0 < |\bracket{v}{\xi_n(\lambda)}| < 1$ (see  Eq.~(\ref{eq:v_xi})).
Hence we have
$
  0 < \partial {E_n(\lambda)}/\partial\lambda < T^{-1}
$
and accordingly
\begin{equation}
  \label{eq:DeltaEnRestriction}
  0 < \Delta E_n < 2\pi T^{-1}.
\end{equation}
This imposes a restriction $0 < \nu < N$ in Eq.~(\ref{eq:quantizedDE0}).
In particular, neither $\nu = 0$ nor $N$ is possible.
Namely, the quasienergy $E_0(\lambda)$ arrives at
$E_{\nu}(\lambda_0)$ ($0 < \nu < N$), instead of $E_0(\lambda_0)$,
as $\lambda\nearrow \lambda_0+2\pi$.
This is nothing but a manifestation of Cheon's anholonomy in quasienergy.

If the system is two-level (i.e., $N = 2$),
the above argument immediately implies $\nu = 1$.
Hence it is straightforward to show that
\begin{equation}
  \label{eq:quasienergyAnholonomyRank1}
  E_n(\lambda_0 + 2\pi-0) = E_{n+1}(\lambda_0) \mod 2\pi T^{-1}
\end{equation}
holds for all $0 \le n < N$.

Equation~(\ref{eq:quasienergyAnholonomyRank1}) remains true for $N>2$.
Its justification requires one to examine a sum rule on
$\set{\Delta E_n}_{n=0}^{N-1}$:
\begin{equation}
  \label{eq:sumRuleRank1}
  \sum_{n=0}^{N-1}\Delta E_n
  = \int_{\lambda_0}^{\lambda_0 + 2\pi} \frac{1}{T} ({\rm Tr} \hat{V})d\lambda
  =\frac{2\pi}{T},
\end{equation}
where we used ${\rm Tr} \hat{V} = 1$ for $\hat{V}=\ket{v}\bra{v}$
with normalized $\ket{v}$.
The sum rule~(\ref{eq:sumRuleRank1}) implies that
Eq.~(\ref{eq:quasienergyAnholonomyRank1}) holds for all $0 \le n < N$,
and vice versa,
where the sum $\sum_{n=0}^{N-1}\Delta E_n$ in Eq.~(\ref{eq:sumRuleRank1})
takes its possible minimal value $2\pi T^{-1}$.
Actually, if we assume that
Eq.~(\ref{eq:quasienergyAnholonomyRank1}) is broken for some $n$,
e.g.,
$E_{n}(\lambda_0 + 2\pi-0) = E_{n+\nu}(\lambda_0) \mod 2\pi/T$
with $1 < \nu < N$,
this contradicts with the sum rule~(\ref{eq:sumRuleRank1}).
Thus the quasienergy anholonomy~(\ref{eq:quasienergyAnholonomyRank1})
for $N$-level quantum maps under
the rank-1 perturbation is revealed completely.

The quasienergy anholonomy~(\ref{eq:quasienergyAnholonomyRank1}) induces
an eigenspace anholonomy, which is expressed by projectors:
\begin{equation}
\ket{\xi_n(\lambda_0 + 2\pi-0)}\bra{\xi_n(\lambda_0 + 2\pi-0)}
= \ket{\xi_{n+1}(\lambda_0)}\bra{\xi_{n+1}(\lambda_0)}.
\end{equation}
Note that $\ket{\xi_{n}(\lambda_0)}$ and $\ket{\xi_{n+1}(\lambda_0)}$
are orthogonal, since the corresponding eigenvalues are different.

Finally, we show an anholonomy in a state vector as a result of
the adiabatic increment of $\lambda$ by the period $2\pi$
from $\lambda=\lambda_0$.
When the initial state is prepared to be
an eigenstate $\ket{\xi_n(\lambda_0)}$, the corresponding final state is
\begin{equation}
  \exp \left\{- i \sum_{j=1}^{M} E_n(\lambda_j) T
    + i \int_{\lambda_0}^{\lambda_0+2\pi} A_n(\lambda) d\lambda
  \right\}
  \ket{\xi_{n+1}(\lambda_0)}.
\end{equation}
If we keep the adiabatic increment of $\lambda$, the state vector
will become parallel with the eigenvector
$\ket{\xi_{n+\nu}(\lambda_0)}$ of $\hat{U}_{\lambda_0}$
after the completion of the $\nu$-th iteration of the periodic increment
and return to the initial eigenstate at the end of the $N$-th iteration.

\section{Examples}
\label{sec:examples}
The simplest example of Cheon's anholonomies occurs in a two-level system.
The Floquet operator of the unperturbed system is
\begin{equation}
  \hat{U}_0 \equiv \ketbra{\uparrow}{\uparrow} + \ket{\downarrow}e^{-i\delta}\bra{\downarrow},
\end{equation}
where $\delta\in(0,2\pi)$ and $T=1$ are assumed.
We employ $\ket{v}=(\ket{\uparrow}-i\ket{\downarrow})/\sqrt{2}$, which satisfies
the conditions (i) and (ii) mentioned in Section~\ref{sec:rank1}.
Although the constant term in
$\hat{V}=\ket{v}\bra{v} = \frac{1}{2}(1-\hat{\sigma}_y)$
seems to be
irrelevant, this term arises naturally in projection operators
in the two-level system and is required to ensure that
the perturbed Floquet operator
$\hat{U}_{\lambda}=\hat{U}_{0} e^{-i\lambda\hat{V}}$
has the $2\pi$ periodicity about $\lambda$.
In order to show an analytic form of quasienergies and eigenvectors,
we employ $\delta=\pi$ (i.e., $\hat{U}_0 = \hat{\sigma}_z$).
The eigenvalues of $\hat{U}_{\lambda}$ are
$z_{0}(\lambda) = e^{-i\lambda/2}$ and
$z_{1}(\lambda) = -e^{-i\lambda/2}$.
The period of each eigenvalue about $\lambda$ is $4\pi$,
though the period of the spectrum $\{z_{0}(\lambda), z_{1}(\lambda)\}$ is
$2\pi$.
The corresponding quasienergies are
\begin{equation}
  \label{eq:sampleE}
  E_{0}(\lambda)= \frac{1}{2}\lambda\mod 2\pi
  \quad\text{and}\quad
  E_{1}(\lambda)= \pi + \frac{1}{2}\lambda\mod 2\pi.
\end{equation}
Now we demonstrate the anholonomy in quasienergy (see Fig.~\ref{fig:twolevel}):
At $\lambda=0$, we start from the quasienergy $E_{0}(0) = 0$ of the 0-th
eigenstate.
The increment of $\lambda$ increases
$E_0(\lambda)$ because of the fact $dE_0(\lambda)/d\lambda = \frac{1}{2} > 0$.
At $\lambda=2\pi$, $E_{0}(\lambda)$ arrives at
$\pi$, which agrees with the quasienergy $E_1(0) = \pi$
of the first eigenstate at $\lambda=0$.
Next, we examine the eigenvectors
\begin{align}
  \label{eq:twoleveleigenvecs}
  \ket{\xi_0(\lambda)} =
  \begin{bmatrix}\cos(\lambda/4)\\ \sin(\lambda/4)\end{bmatrix},
  \quad
  \ket{\xi_1(\lambda)} =
  \begin{bmatrix}-\sin(\lambda/4)\\ \cos(\lambda/4)\end{bmatrix}.
\end{align}
The corresponding geometric gauge potentials $A_{n}(\lambda)$ ($n=0,1$)
happen to vanish in the present case. Hence it is easy to
find the geometric phases from
the parametric dependence of the eigenvectors~(\ref{eq:twoleveleigenvecs}).
The excursion of the eigenvectors by increasing the parameter $\lambda$
is the following:
\begin{align}
  \ket{\xi_{0}(0)} &= \ket\uparrow,&\quad
  \ket{\xi_{1}(0)} &= \ket\downarrow,
  \nonumber \\
  \ket{\xi_{0}(2\pi)} &= \ket{\xi_{1}(0)},&\quad
  \ket{\xi_{1}(2\pi)} &= -\ket{\xi_{0}(0)},
  \\
  \ket{\xi_{0}(4\pi)} &= - \ket{\xi_{0}(0)},&\quad
  \ket{\xi_{1}(4\pi)} &= -\ket{\xi_{1}(0)},
  \nonumber
\end{align}
where nontrivial geometric phases appear after the completion
of the $4\pi$ increment of $\lambda$.

\begin{figure}

  \includegraphics[width=8.6cm]{fig1a}
  \hfill
  \includegraphics[width=8.6cm]{fig1b}
  \caption{\label{fig:twolevel} (Color online)
    Parametric motions of quasienergies (bold lines) of two-level systems.
    We choose the model whose ``ground'' quasienergy is zero at $\lambda = 0$.
    The other quasienergy $\delta=\pi$ at $\lambda = 0$ is indicated
    by the broken, horizontal lines.
    (a) The example examined in the main text, Eq.~(\ref{eq:sampleE})
    ($\ket{v}=(\ket{\uparrow}-i\ket{\downarrow})/\sqrt{2}$).
    The quasienergies draw two parallel lines, which have no
    avoided crossing.
    (b) A generic example
    ($\ket{v} = \cos(\pi/8)\ket{\uparrow} + \sin(\pi/8)\ket{\downarrow}$).
    There is a single avoided crossing. The broken curve represents
    $|\bracket{\uparrow}{\xi_0(\lambda)}|^2$, which depicts
    that $\ket{\xi_0(\lambda)}$
    becomes orthogonal to $\ket{\xi_0(0)}$ in
    the limit $\lambda \uparrow 2\pi$.
  }
\end{figure}

We suggest a possible implementation of
the example above in a charged particle with a spin-$1/2$.
Assume that the particle is localized to some place so that we may
ignore the motion of the particle.
The unperturbed system is the spin under a static magnetic
field. The perturbation $\hat{V}$ is composed of two ingredients:
One is a periodically pulsed magnetic field, whose direction needs to be
different from that of the unperturbed magnetic field.
The other is
a periodically pulsed electric field, which provides
``the constant part'' of $\hat{V}$. In order to prepare $\hat{V}$,
we need to adjust the ratio of the strength and the period of
the two perturbation fields.

Finally, we show another example that involves multiple levels
in Fig.~\ref{fig:multilevel} (a), where all quasienergies are involved
in the anholonomy.
This is due to the cyclicity of $\ket{v}$.
In Fig.~\ref{fig:multilevel}~(b), we also show an
example that breaks the cyclicity of $\ket{v}$.
This suggests that we may control the anholonomy to the limited number of
states by an appropriate choice of $\ket{v}$.

\begin{figure}

  \includegraphics[width=8.6cm]{fig2a}
  \hfill
  \includegraphics[width=8.6cm]{fig2b}
  \caption{\label{fig:multilevel} (Color online)
    Parametric motions of quasienergies (bold lines) in systems
    with multiple levels ($\dim\mathcal{H} = 5$).
    The unperturbed Floquet operator $\hat{U}_0$,
    whose ``ground'' quasienergy is adjusted to zero at $\lambda = 0$,
    is randomly chosen.
    The quasienergies at $\lambda = 0$ are indicated by the broken,
    horizontal lines.
    (a) A random choice of $\ket{v}$, which satisfies cyclicity for
    $\hat{U}_0$.
    All quasienergies exhibit anholonomy.
    (b) An example for broken cyclicity in $\ket{v}$:
    Only three components of $\ket{v}$, in the representation
    that diagonalizes $\hat{U}_0$, take nonzero values.
    The resultant parametric changes and anholonomy occur only in
    the subspace ${\rm span} \set{\hat{U}_0^m\ket{v}}_{m}$,

    whose dimensionality is three.
    The other two quasienergies draw horizontal lines,
    since they correspond to the trivial eigenvectors mentioned
    in Section~\ref{sec:rank1},
    and are not affected by the perturbation.

  }
\end{figure}

\section{Geometry and abundance of quasienergy anholonomy}
\label{sec:abundance}

We remark on the geometry of the quasienergy anholonomy to discuss its
stability and abundance.
Concerning Cheon's eigenenergy anholonomy in a family of systems with
generalized pointlike potentials,
Tsutsui, F\"ulop, and Cheon examined the geometry of the anholonomy
using the fact that the parameter space of the family is
$U(2)$~\cite{Cheon:AP-294-1,Tsutsui:JMP-42-5687}.
When the dimension of the Hilbert space is two,
Tsutsui {\it et al.}'s argument is immediately applicable to the
quasienergy anholonomy in the systems whose unit time evolution is
described by a Floquet operator, which is a $2\times2$ unitary
matrix.
We employ a parametrization of such systems by
their quasienergy-spectrum $\{(E_0, E_1)\}$~(Fig.~\ref{fig:geometry} (a)),
whose element $(E_0, E_1)$ is identified with $(E_1, E_0)$.
The quotient quasienergy-spectrum space is accordingly
an orbifold $T^2/\bbset{Z}_2$
which has two topologically inequivalent and nontrivial
cycles (see  Fig.~\ref{fig:geometry} (c) and Ref.~\cite{Tsutsui:JMP-42-5687}).
One cycle traverses the degeneracy line $E_0 = E_1$.
The other cycle concerns the ``increment'' (or ``decrement'') of
the quantum number.
More precisely,
the winding number along the latter cycle determines the increment of
the quantum number (Fig.~\ref{fig:geometry} (d)).
When the dimension of Hilbert space is  larger than 2,
similar geometrical argument will be possible.
The geometrical nature implies that the quasienergy anholonomy is
stable against perturbations that preserves the topology of the cycle.
Hence we may expect that the same anholonomy appears in
nonautonomous systems whose unit time evolution is described by
a Floquet operator, e.g., periodically kicked systems and periodically driven
systems.

The stability of Cheon's anholonomies against perturbations is also
expected from the fact
that the parametric dependence of the quasienergies has no crossings
(see Figs.~\ref{fig:twolevel} and \ref{fig:multilevel}~(a)).
To achieve the stability in practice, the gap of narrowly avoided
crossings needs to be enlarged. This is possible with a
suitable adjustment of $\ket{v}$
(e.g., see Figs.~\ref{fig:twolevel} (a) and (b)).
We also remark that the presence of the trivial eigenvectors,
which are introduced in Section~\ref{sec:rank1},
induces the crossings of quasienergies, as can be seen in
Fig.~\ref{fig:multilevel}~(b) and in Appendix~\ref{sec:normalForm}.
Hence quasienergy anholonomies coexisting with trivial eigenvectors
are fragile against perturbations in general.

\begin{figure}

  \includegraphics[width=4.22cm]{fig3a}
  \
  \includegraphics[width=4.22cm]{fig3b}
  \\[\baselineskip]

  \includegraphics[width=4.22cm]{fig3c}
  \
  \includegraphics[width=4.22cm]{fig3d}

  \caption{\label{fig:geometry} (Color online)
    A parametrization with the quasienergy-spectrum of quantum systems whose
    unit time evolutions are described by two-dimensional Floquet operators
    is explained.
    (a) An $E_0-E_1$ plane, where a and a' are at
    $(0, 2\pi/T)$ and $(2\pi/T, 0)$, respectively.
    Because of the periodicity of quasienergies, pairs of lines
    Oa and a'O', and, Oa' and aO' are identified.
    On the diagonal line $E_0 = E_1$, two quasienergies are degenerate.
    In the subsequent figures, $(E_0, E_1)$ and $(E_1, E_0)$ are identified.

    (b) $\triangle$Oba' and $\triangle$O'ba are identified with
    $\triangle$Oba and $\triangle$O'ba', respectively, and so are removed.
    (c) The quotient space  $T^2/\bbset{Z}_2$.
    Since Oa and a'O' in (b) are identical, they are arranged to make
    a square. Furthermore, if identical lines Ob' and ab are put
    together, a M\"obius strip with edges Ob and ab', which are
    degenerate lines, is obtained
    (see Ref.~\cite{Tsutsui:JMP-42-5687}).
    (d) Parametric motion of spectrum on $T^2/\bbset{Z}_2$.
    Bold and dashed lines, which are topologically equivalent
    on the M\"obius strip, correspond to
    Figs.~\ref{fig:twolevel} (a) and (b), respectively, where
    $T=1$ is assumed. At $\lambda=0$,
    they start from the open circle at $(0, \pi)$. As $\lambda$ increases,
    they move toward ab. At $\lambda=\pi$, they arrive on a point on a line
    ab, which is identical with $Ob'$. Then they return to $(0, \pi)$.
    Such a winding along the M\"obius strip induces the quasienergy
    anholonomy.
  }
\end{figure}

\section{Application: anholonomic quantum state manipulation}
\label{sec:manipulation}

As an application of the quasienergy anholonomy, a design principle of
systems that achieve manipulations of quantum states with adiabatic passages
is proposed.
Before describing our argument, we mention that the conventional
works on the application of adiabatic passages to the manipulation of
quantum states are the textbook results~\cite{QuantumControlTexts}.
At the same time, there are interesting proposals on quantum circuits
whose elementary operations are composed by adiabatic processes%
~\cite{AdiabaticControl}.
The reason why the adiabatic processes are employed is that
the operations governed by the adiabatic processes are
expected to be stable.
On the other hand, the manipulation that involves the phase anholonomy
is expected to be stable under the perturbation, due to its topological
nature.

Our scheme proposed here also relies on the adiabatic processes and
employs nonconventional, Cheon's anholonomies in quantum maps.
The aim is to evolve a quantum state (``the initial target'')
into another state (``the final target'').
What we need to carry it out is twofold:
One is an ``unperturbed'' Hamiltonian $\hat{H}_0$, whose eigenstates
must contain the two target states.
The other is a normalized vector $\ket{v}$, which must have
nonzero overlappings between the two target states.
Under the influence of a periodically pulsed perturbation
$\hat{V}=\ketbra{v}{v}$ with its period $T$ and strength $\lambda$,
the system is described
by the kicked Hamiltonian $\hat{H}(t)$~(\ref{eq:kickedHamiltonian}).
The use of the quasienergy anholonomy of
the corresponding Floquet operator $\hat{U}_{\lambda}$~(\ref{eq:defUlambda})
is straightforward
if  $\hat{H}_0$ is bounded and contains only discrete eigenenergies
and $T$ is smaller than $2\pi\hbar/W$, where
$W$ is the difference between the maximum and the minimum eigenenergies
of $\hat{H}_0$.
Otherwise, we need to achieve these conditions effectively,
by adjusting $\ket{v}$.
For example, $\ket{v}$ needs to be prepared to have no overlapping
with the eigenstates that have higher eigenergies to make
an effective energy cutoff on $\hat{H}_0$.

Once we prepare such $\hat{U}_{\lambda}$, it is straightforward to
realize the manipulation, at least, in theory.
To convert a state vector, which is initially in
an eigenstate of $\hat{U}_0$, to the nearest higher eigenstate
of $\hat{U}_0$, is achieved by applying the periodically pulsed perturbation
$\hat{V}=\ketbra{v}{v}$,
whose strength $\lambda$ is adiabatically increased from 0 to $2\pi$.
Note that at the final stage of the manipulation, we may switch off
the perturbation suddenly, due to the periodicity of the
Floquet operator $\hat{U}_{2\pi} = \hat{U}_{0}$.
This closes a ``cycle.''
By repeating the cycle, the final state can be
any eigenstate of $\hat{U}_0$.
Note that, along the operation, $\ket{v}$ may vary adiabatically.
In other words, the adiabatically slow fluctuation on $\ket{v}$
does no harm.
We remark that an application of the present procedure to anholonomic
adiabatic quantum computation is described in a separate
publication~\cite{TM061}.

The strongest limitations of the present scheme,
in our opinion, is that the target states for the manipulation
must be eigenstates of $\hat{H}_0$.
Superpositions of the eigenstates of $\hat{H}_0$ cannot be the targets
due to the presence of dynamical phases that generally diverge in adiabatic
processes.
Note that, however, there is no obstacle to
handle ``superposed states'' when they are eigenstates of $\hat{H}_0$.
Furthermore, if we could introduce Cheon's anholonomies to
the systems whose quasienergy are degenerate, it may be possible to
carry out a coherent manipulation within a degenerate eigenspace.
This motivates us to seek an extension of the eigenspace anholonomy
for degenerate eigenspace,
i.e., Cheon's anholonomies \'a la Wilczek and Zee.

\section{Discussion and summary}
\label{sec:summary}

We have discussed Cheon's anholonomies in a family of quantum
map~(\ref{eq:expandUlambda}) with a rank-one projection $\hat{V}$.
Although our geometrical argument in Section~\ref{sec:abundance} assures
the abundance of the systems that exhibit the anholonomies,
we still do not have any systematic way to find such systems,
except the quantum map~(\ref{eq:expandUlambda}).
In order to suggest exploring other examples of the anholonomies,
we summarize conditions to find the anholonomies.
Two ingredients in our Floquet operator~(\ref{eq:expandUlambda})
facilitate us to find the anholonomies:
(a) the periodicity of the Floquet operator for the parameter $\lambda$
enforces the periodicity of the spectrum;
and (b) the positivity of the perturbation assures the monotonic increment
of each quasienergy for the increment of $\lambda$.
These two facts imply that $E_n(\lambda)$ arrives at a higher excited
quasienergy $E_{n + \delta n}(\lambda)$ ($\delta n>0$)
after an increment of $\lambda$ by the period $2\pi$.
To realize the first condition, $\hat{V}$ needs not to be a
projection operator. For the Floquet operator~(\ref{eq:defUlambda}),
the condition for the periodicity is
$e^{-i \Lambda\hat{V}/\hbar} = 1$, where $\Lambda$ is the period.
In terms of the eigenvalues $\set{v_n}_n$ of $\hat{V}$, this condition
is that $\Lambda v_n / (2\pi\hbar)$ is an integer for all $n$.
Although we suppose that the anholonomies may be realized without
the condition (b), we are not aware of any examples,
except the trivial cases, e.g., $\hat{V}$ is negative definite.
Furthermore, the above two conditions generally do not determine the exact
value of $\delta n$, which is the increment of the quantum number
after a single cycle,
whereas $\delta n=1$ for a rank-1 projection $\hat{V}$ is
shown in Section~\ref{sec:existance}.
The value of $\delta n$ could be determined by the geometric
argument shown in Section~\ref{sec:abundance}.
However, no systematic algorithm to compute $\delta n$
from a given family of Floquet operators is known to us.

\begin{acknowledgments}
  M.M. would like to thank Professor I. Ohba and Professor H. Nakazato
  for useful comments.
  A.T. wishes to thank Professor A.~Shudo, Professor K.~Nemoto, and
  Professor M.~Murao for useful conversations.
\end{acknowledgments}

redpajama_set_name: RedPajamaArXiv


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I'm now 31 weeks pregnant which means in two months time there's going to be a little bub in the house. Suddenly there's a million and one things to do; painting, purchasing baby items, moving furniture around including relocating my husband's study to the lounge room.. the list goes on. Fairly low down the list is the priority to make things. I have fabric and wool to whip up some simple quilts and rugs, but while I'm still working full time there just doesn't seem to be enough time for craft while getting the house ready at the same time. So let's call it an unintentional craft hiatus which I'm sure will be over in 5 weeks when my mat leave begins.
In the meantime, I have been somewhat creative; we've just done a mini reno on our laundry cupboard which involved a coat of paint, relocation of some stupidly placed shelves that blocked the light and installation of lots of new shelves, railings and gadget holders. I'm so pleased with the result. My only regret is not having a 'before' photo.
As you can see, our 'laundry' is actually located in a cupboard in the bathroom. None of the shelves you see were there previously and the walls were an interesting salmony pink. It's so nice no longer needing to store the washing liquid on the floor and the iron on the washing machine! There's storage space to the left where the vacuum cleaner, mop, duster etc live, along with a couple more shelves. The top one is holding some of my ridiculous amount of Christmas decorations. The rest of those are going under the house to make room for Col's new study area.