Biography:Frank Wilczek

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Short description: American physicist and Nobel laureate (born 1951)
Frank Wilczek
FrankStockholm2004.jpg
Wilczek in 2004
Born
Frank Anthony Wilczek

(1951-05-15) May 15, 1951 (age 73)
Mineola, New York, U.S.
EducationUniversity of Chicago (BS)
Princeton University (MA, PhD)
Known forAsymptotic freedom
Quantum chromodynamics
Particle statistics
Axion model
Spouse(s)Betsy Devine
ChildrenAmity and Mira[1]
AwardsMacArthur Fellowship (1982)
Sakurai Prize (1986)
ICTP Dirac Medal (1994)
Lorentz Medal (2002)
Lilienfeld Prize (2003)
Nobel Prize in Physics (2004)
King Faisal Prize (2005)
Templeton Prize (2022)
Scientific career
FieldsPhysics
Mathematics
InstitutionsMIT
T. D. Lee Institute and Wilczek Quantum Center, Shanghai Jiao Tong University
Arizona State University
Stockholm University
ThesisNon-abelian gauge theories and asymptotic freedom (1974)
Doctoral advisorDavid Gross
Websitefrankawilczek.com

Frank Anthony Wilczek (/ˈvɪltʃɛk/[2] or /ˈwɪltʃɛk/;[3] born May 15, 1951) is an American theoretical physicist, mathematician and Nobel laureate. He is the Herman Feshbach Professor of Physics at the Massachusetts Institute of Technology (MIT), Founding Director of T. D. Lee Institute and Chief Scientist at the Wilczek Quantum Center, Shanghai Jiao Tong University (SJTU), distinguished professor at Arizona State University (ASU) and full professor at Stockholm University.[4]

Wilczek, along with David Gross and H. David Politzer, was awarded the Nobel Prize in Physics in 2004 "for the discovery of asymptotic freedom in the theory of the strong interaction".[5] In May 2022, he was awarded the Templeton Prize for his investigations into the fundamental laws of nature, that have transformed our understanding of the forces that govern our universe and revealed an inspiring vision of a world that embodies mathematical beauty.[6]

Early life and education

Born in Mineola, New York, Wilczek is of Polish and Italian origin.[1] His grandparents were immigrants who "really did work with their hands", according to Wilczek, but Frank's father took night school classes to educate himself, working as a repairman to support his family.[7] Wilczek's father became a "self-taught engineer", whose interests in technology and science inspired his son.[8]

Wilczek was educated in the public schools of Queens, attending Martin Van Buren High School. It was around this time Wilczek's parents realized that he was exceptional—in part as a result of Frank Wilczek having been administered an IQ test.[9]

After skipping two grades, Wilczek started high school in the 10th grade, when he was 13 years old. He was particularly inspired by two of his high school physics teachers, one of whom taught a course that helped students with the national Westinghouse Science Talent Search. Wilczek was a finalist in 1967 and ultimately won fourth place, based on a mathematical project involving group theory.[10][11]

He received his Bachelor of Science in Mathematics and membership in Phi Beta Kappa[12] at the University of Chicago in 1970. During his last year as a math major at Chicago, he attended a course taught by Peter Freund on group theory in physics, which Wilczek later described as being "basically particle physics", and very influential:[7]

Peter Freund played a big role in my life, though, because he taught this course on group theory, or symmetry in physics that—he was so enthusiastic, and he really gushed—and it's beautiful material. Still to this day I think the quantum theory of angular momentum is one of the absolute pinnacles of human achievement. Just beautiful.

Wilczek went to Princeton as a mathematics graduate student. After a year and a half, he transferred from mathematics to physics, with David Gross as his thesis advisor.[7]

He earned a Master of Arts in Mathematics in 1972 and a Ph.D. in physics in 1974, both from Princeton University.[13]

Personal life

Wilczek met Betsy Devine at Princeton, when both watched the televised 1972 Fisher-Spassky chess matches.[14] They married in 1973, and together they have two daughters.[1] His favorite physicist is James Clerk Maxwell.[15]

Religious views

Wilczek was raised Catholic but later "lost faith in conventional religion"[1] although he told Scientific American that religion "had meant a lot to me as a teenager".[16] He has been described as an agnostic[17] but tweeted in 2013 that "pantheist" is "closer to the mark".[18]

Wilczek said that "the world embodies beautiful ideas" but "although this may inspire a spiritual interpretation, it does not require one".[19][20]

Science outreach and activism

Wilczek is a member of the Scientific Advisory Board for the Future of Life Institute, an organization that works to mitigate existential risks facing humanity, particularly existential risk from advanced artificial intelligence.[21]

In 2014, Wilczek penned a letter, along with Stephen Hawking and two other scholars, warning that "Success in creating AI would be the biggest event in human history. Unfortunately, it might also be the last, unless we learn how to avoid the risks."[22]

Wilczek is also a supporter of the Campaign for the Establishment of a United Nations Parliamentary Assembly, an organization which advocates for democratic reform in the United Nations, and the creation of a more accountable international political system.[23]

Wilczek is on the board for Society for Science & the Public. He is a co-founding member of the Kosciuszko Foundation of the Collegium of Eminent Scientists of Polish Origin and Ancestry.[24]

Wilczek has appeared on an episode of Penn & Teller: Bullshit!, where Penn referred to him as "the smartest person [they have] ever had on the show".

Honors

In 1982, he was awarded a MacArthur Fellowship.[25]

Wilczek was elected as a member of the National Academy of Sciences in 1990, a member of the American Academy of Arts and Sciences in 1993,[26][27] and the American Philosophical Society in 2005.[28]

Wilczek became a foreign member of the Royal Netherlands Academy of Arts and Sciences in 2000.[29] He was awarded the Lorentz Medal in 2002. Wilczek won the Lilienfeld Prize of the American Physical Society in 2003. In the same year he was awarded the Faculty of Mathematics and Physics Commemorative Medal from Charles University in Prague. He was the co-recipient of the 2003 High Energy and Particle Physics Prize of the European Physical Society. The Nobel Prize in Physics 2004 was awarded jointly to David J. Gross, H. David Politzer and Frank Wilczek "for the discovery of asymptotic freedom in the theory of the strong interaction". Wilczek was also the co-recipient of the 2005 King Faisal International Prize for Science. In that same year, he received the Golden Plate Award of the American Academy of Achievement.[30] On January 25, 2013, Wilczek received an honorary doctorate from the Faculty of Science and Technology at Uppsala University, Sweden.[31] He also served on the Physical Sciences jury for the Infosys Prize from 2009 to 2011. In 2011, Wilczek gave the George Gamow Memorial Lecture at the University of Colorado Boulder.[32] In 2022 he was awarded the Templeton Prize[33] for work that reveals "a vision of a universe that he regards as embodying mathematical beauty at the scales of the magnificently large and unimaginably small".[34]

Wilczek holds the Herman Feshbach Professorship of Physics at MIT Center for Theoretical Physics. He has also worked at the Institute for Advanced Study in Princeton and the Institute for Theoretical Physics at the University of California, Santa Barbara and was also a visiting professor at NORDITA.

Research

Wilczek's 2004 Nobel Prize was for asymptotic freedom, but he has helped reveal and develop axions, anyons, asymptotic freedom, the color superconducting phases of quark matter, and other aspects of quantum field theory. He has worked on condensed matter physics, astrophysics, and particle physics.

Asymptotic freedom

In 1973, while a graduate student working with David Gross at Princeton University, Wilczek (together with Gross) discovered asymptotic freedom, which holds that the closer quarks are to each other, the less the strong interaction (or color charge) between them; when quarks are in extreme proximity, the nuclear force between them is so weak that they behave almost as free particles. The theory, which was independently discovered by H. David Politzer, was important for the development of quantum chromodynamics. According to the Royal Netherlands Academy of Arts and Sciences when awarding Wilczek its Lorentz Medal in 2002,[35]

This [asymptotic freedom] is a phenomenon whereby the building blocks which make up the nucleus of an atom – 'quarks' – behave as free particles when they are close together, but become more strongly attracted to each other as the distance between them increases. This theory forms the key to the interpretation of almost all experimental studies involving modern particle accelerators.

Axions

Main page: Physics:Axion

The axion is a hypothetical elementary particle. If axions exist and have low mass within a specific range, they are of interest as a possible component of cold dark matter.

In 1977, Roberto Peccei and Helen Quinn postulated a solution to the strong CP problem, the Peccei–Quinn mechanism. This is accomplished by adding a new global symmetry (called a Peccei–Quinn symmetry.) When that symmetry is spontaneously broken, a new particle results, as shown independently by Wilczek and by Steven Weinberg.[36][37] Wilczek named this new hypothetical particle the "axion" after a brand of laundry detergent,[38] while Weinberg called it "Higglet". Weinberg later agreed to adopt Wilczek's name for the particle.[39]

Although most experimental searches for dark matter candidates have targeted WIMPs, there have also been many attempts to detect axions.[40] In June, 2020, an international team of physicists working in Italy detected a signal that could be axions.[41][42]

Anyons

Main page: Anyon

In physics, an anyon is a type of quasiparticle that occurs only in two-dimensional systems, with properties much less restricted than fermions and bosons. In particular, anyons can have properties intermediate between fermions and bosons, including fractional electric charge. This anything-goes behavior inspired Wilczek in 1982 to name them "anyons".[43]

In 1977, a group of theoretical physicists working at the University of Oslo, led by Jon Leinaas and Jan Myrheim, calculated that the traditional division between fermions and bosons would not apply to theoretical particles existing in two dimensions.[44] When Daniel Tsui and Horst Störmer discovered the fractional quantum Hall effect in 1982, Bertrand Halperin (1984) expanded the math Wilczek proposed in 1982 for fractional statistics in two dimensions to help explain it.[45]

Frank Wilczek, Dan Arovas, and Robert Schrieffer analyzed the fractional quantum Hall effect in 1984, proving that anyons were required to describe it.[46][47]

In 2020, experimenters from the Ecole Normale Supérieure and from the Centre for Nanosciences and Nanotechnologies (C2N) reported in Science that they had made a direct detection of anyons.[46][48]

Time crystals

Main page: Physics:Time crystal

In 2012 he proposed the idea of a time crystal.[49] In 2018, several research teams reported the existence of time crystals.[50] In 2018 he and Qing-Dong Jiang calculated that the so-called "quantum atmosphere" of materials should theoretically be capable of being probed using existing technology such as diamond probes with nitrogen-vacancy centers.[51][52]

Current research

Publications

For lay readers

Technical

  • 1988. Geometric Phases in Physics.
  • 1990. Fractional Statistics and Anyon Superconductivity.[54]

See also

References

  1. ↑ 1.0 1.1 1.2 1.3 "Frank Wilczek – Autobiography". Nobel Prize. https://www.nobelprize.org/prizes/physics/2004/wilczek/biographical/. 
  2. ↑ Wilczek, Frank. 2004 Nobel Highlights with Laureates in Physics, David J. Gross, H. David Politzer, Frank Wilczek. Nobel Prize. Event occurs at 0:42 – via YouTube.
  3. ↑ Wilczek, Frank. A Beautiful Question. Talks at Google. Event occurs at 0:13 – via YouTube.
  4. ↑ "Frank Wilczek, Herman Feshbach Professor of Physics". Department of Physics, MIT. 2011. http://web.mit.edu/physics/people/faculty/wilczek_frank.html. 
  5. ↑ "Frank Wilczek Facts". Stockholm: Nobel Foundation. https://www.nobelprize.org/prizes/physics/2004/wilczek/facts/. 
  6. ↑ Thomas, Burnett (May 11th, 2022). "Dr. Frank Wilczek Receives 2022 Templeton Prize", The Templeton Prize. Retrieved 11 May 2022.
  7. ↑ 7.0 7.1 7.2 Wilczek, Frank (September 15, 2020). "Oral history interview with Frank Wilczek, 2020 June 4". AIP. https://www.aip.org/history-programs/niels-bohr-library/oral-histories/44536. "Somewhere between working class and lower middle class. Yeah, lower middle class, I guess I would say. Unlike my grandparents, who really did work with their hands, my father, as I said, was kind of a technician and repairman. He actually got very good at the job and was rising through the ranks." 
  8. ↑ "The Nobel laureate who got hooked on Stockholm". Stockholm University. September 15, 2020. https://www.su.se/english/research/profile-areas/astrophysics-cosmology-and-particle-physics/the-nobel-laureate-who-got-hooked-on-stockholm-1.309112. "Frank Wilczek’s story starts in Queens, New York, where he grew up in a working-class family with roots in Europe. They were children of the Great Depression from Long Island and had limited access to resources, but that didn't stop them from working to educate themselves. Frank’s father was a self-taught engineer and passed his interest in technology and science on to his son." 
  9. ↑ Dreifus, Claudia (December 28, 2009). "Discovering the Mathematical Laws of Nature". The New York Times. https://www.nytimes.com/2009/12/29/science/29conv.html?_r=1. 
  10. ↑ "Noteworthy graduates: Frank Wilczek, Nobel laureate in physics". United Federation of Teachers. December 7, 2018. https://www.uft.org/news/feature-stories/noteworthy-graduates/noteworthy-graduates-frank-wilczek-nobel-laureate-physics. "As a high school senior, Wilczek was a finalist in the national Science Talent Search. He says his premise about mathematical structures called groups was the best part of his project, posing 'a sensible question for someone to ask at that stage'." 
  11. ↑ "Westinghouse Science Talent Search 1967". Society for Science. https://www.societyforscience.org/regeneron-sts/science-talent-search-1967/. 
  12. ↑ "FRANK WILCZEK CURRICULUM VITAE – PDF". https://docplayer.net/31086301-Frank-wilczek-curriculum-vitae.html. 
  13. ↑ Frank Anthony Wilczek at the Mathematics Genealogy Project
  14. ↑ Thompson, Elizabeth A (October 5, 2004). "Wilczek thanks family, country and Mother Nature". MIT News. https://news.mit.edu/2004/nobel-conf. "'I noticed that whatever moves Frank called out, the players would do what he said. They'd make the moves he predicted. This happened even when what he called out was different from what others called out', recalled Devine." 
  15. ↑ Wilczek, Frank (2015). A Beautiful Question. 
  16. ↑ Merali, Zeeya (May 11, 2022). "God, Dark Matter and Falling Cats: A Conversation with 2022 Templeton Prize Winner Frank Wilczek". Scientific American. https://www.scientificamerican.com/article/god-dark-matter-and-falling-cats-a-conversation-with-2022-templeton-prize-winner-frank-wilczek/. Retrieved June 12, 2022. "The use of the word “God” in common culture is very loose. People can mean entirely different things by it. For me, the unifying thread is thinking big: thinking about how the world works, what it is, how it came to be and what all that means for what we should do. I chose to study this partly to fill the void that was left when I realized I could no longer accept the dogmas of the Catholic Church that had meant a lot to me as a teenager.". 
  17. ↑ Wang, Amy X. (4 August 2015). "Why Is the World So Beautiful? A Physicist Tries to Answer.". https://slate.com/culture/2015/08/frank-wilczeks-a-beautiful-question-reviewed.html. 
  18. ↑ Wilczek, Frank [@FrankWilczek] (September 8, 2013). "My Wikipedia entry says "agnostic", but "pantheist" is closer to the mark. Spinoza, Beethoven, Walt Whitman, Einstein – good company!". https://twitter.com/FrankWilczek/status/376705595228696576. 
  19. ↑ 'A Beautiful Question', pp. 1–3, 322
  20. ↑ "A theoretical physicist searches for the design behind nature's beauty". Slate. http://www.slate.com/articles/arts/books/2015/08/frank_wilczek_s_a_beautiful_question_reviewed.html. 
  21. ↑ Who We Are, Future of Life Institute, 2014, http://thefutureoflife.org/who, retrieved 2014-05-07 
  22. ↑ "Stephen Hawking: 'Transcendence looks at the implications of artificial intelligence – but are we taking AI seriously enough?'". The Independent (UK). 1 May 2014. https://www.independent.co.uk/news/science/stephen-hawking-transcendence-looks-at-the-implications-of-artificial-intelligence-but-are-we-taking-9313474.html. 
  23. ↑ "Overview" (in en-US). Campaign for a UN Parliamentary Assembly. http://en.unpacampaign.org/supporters/overview/page/5/?mapcountry=allpro&mapgroup=pro. 
  24. ↑ "Kosciuszko Foundation - American Center of Polish culture - Eminent Scientists of Polish Origin and Ancestry". https://www.thekf.org/kf/programs/eminentscientists/. 
  25. ↑ "Frank Wilczek – MacArthur Foundation". https://www.macfound.org/fellows/130/. 
  26. ↑ "Frank Wilczek". http://www.nasonline.org/member-directory/members/46075.html. 
  27. ↑ "Frank Wilczek" (in en). https://www.amacad.org/person/frank-wilczek. 
  28. ↑ "APS Member History". https://search.amphilsoc.org/memhist/search?creator=Frank+Wilczek&title=&subject=&subdiv=&mem=&year=&year-max=&dead=&keyword=&smode=advanced. 
  29. ↑ "F.A. Wilczek". Royal Netherlands Academy of Arts and Sciences. https://www.knaw.nl/en/members/foreign-members/5112. 
  30. ↑ "Golden Plate Awardees of the American Academy of Achievement". American Academy of Achievement. https://achievement.org/our-history/golden-plate-awards/#science-exploration. 
  31. ↑ "New honorary doctorates in science and technology – Uppsala University, Sweden". http://www.uu.se/en/research/grants-awards/article/?id=2263&area=12,16&typ=artikel&lang=en. 
  32. ↑ Anas, Brittany (April 18, 2011). "Nobel Prize Winner Frank Wilczek to lecture at CU Boulder". Daily Camera. https://www.dailycamera.com/2011/04/18/nobel-prize-winning-physics-professor-frank-wilczek-to-lecture-at-cu-boulder/. 
  33. ↑ "Frank Wilczek". Templeton Prize. 2022. https://www.templetonprize.org/laureate/frank-wilczek/. 
  34. ↑ "Nobel physics laureate Frank Wilczek wins Templeton Prize for work on science, spirituality links" (in en-US). The Washington Times. https://www.washingtontimes.com/news/2022/may/11/frank-wilczek-nobel-physics-laureate-wins-templeto/. 
  35. ↑ "Frank Wilczek". Royal Netherlands Academy of Arts and Sciences. 2002. https://www.knaw.nl/en/awards/laureates/lorentzmedaille/lorentzmedaille-2002-voor-amerikaanse-fysicus. 
  36. ↑ Wilczek, F. (1978). "Problem of Strong P and T Invariance in the Presence of Instantons". Physical Review Letters 40 (5): 279–282. doi:10.1103/PhysRevLett.40.279. Bibcode: 1978PhRvL..40..279W. 
  37. ↑ Weinberg, Steven (1978). "A New Light Boson?". Physical Review Letters 40 (4): 223–226. doi:10.1103/PhysRevLett.40.223. Bibcode: 1978PhRvL..40..223W. 
  38. ↑ Overbye, Dennis (17 June 2020). "Seeking dark matter, they detected another mystery". The New York Times. https://www.nytimes.com/2020/06/17/science/xenon-axions-neutrinos-tritium.html. 
  39. ↑ Wilczek, Frank (7 January 2016). "Time's (almost) reversible arrow". Quanta Magazine. https://www.quantamagazine.org/how-axions-may-explain-times-arrow-20160107/. Retrieved 17 June 2020. 
  40. ↑ "Homing in on Axions?" (Physics.aps.org, April 9, 2018)
  41. ↑ Letzter, Rafi (June 17, 2020). "Physicists Announce Potential Dark Matter Breakthrough". Scientific American. https://www.scientificamerican.com/article/physicists-announce-potential-dark-matter-breakthrough/. "A team of physicists has made what might be the first-ever detection of an axion. Axions are unconfirmed, hypothetical ultralight particles from beyond the Standard Model of particle physics, which describes the behavior of subatomic particles. Theoretical physicists first proposed the existence of axions in the 1970s in order to resolve problems in the math governing the strong force, which binds particles called quarks together. But axions have since become a popular explanation for dark matter, the mysterious substance that makes up 85% of the mass of the universe, yet emits no light." 
  42. ↑ Falk, Dan (June 23, 2020). "Is Dark Matter Made of Axions?". Scientific American. https://www.scientificamerican.com/article/is-dark-matter-made-of-axions/. "Then, in 1977 Helen Quinn and the late Roberto Peccei, both then at Stanford University, proposed a solution: perhaps there is a hitherto unknown field that pervades all of space and suppresses the neutron’s asymmetries. Later, theoretical physicists Frank Wilczek and Steven Weinberg deduced that if the Standard Model were tweaked to allow such a field, it would imply the existence of a new particle, dubbed the axion. (Wilczek got the idea for the name from a brand of laundry detergent.)" 
  43. ↑ "Anyons, anyone?". Symmetry Magazine. August 31, 2011. https://www.symmetrymagazine.org/breaking/2011/08/31/anyons-anyone. "In 1982 physicist Frank Wilczek gave these interstitial particles the name anyon ... 'Any anyon can be anything between a boson or a fermion', Keilmann says. 'Wilczek is a funny guy.'" 
  44. ↑ Wilczek, Frank (January 2006). "From electronics to anyonics". Physics World 19 (1): 22–23. doi:10.1088/2058-7058/19/1/31. ISSN 0953-8585. http://physicsworld.com/cws/article/indepth/23894. Retrieved September 25, 2020. "In the early 1980s I named the hypothetical new particles 'anyons', the idea being that anything goes – but I did not lose much sleep anticipating their discovery. Very soon afterwards, however, Bert Halperin at Harvard University found the concept of anyons useful in understanding certain aspects of the fractional quantum Hall effect, which describes the modifications that take place in electronics at low temperatures in strong magnetic fields.". 
  45. ↑ Halperin, B. I. (1984). "Statistics of Quasiparticles and the Hierarchy of Fractional Quantized Hall States". Physical Review Letters 52 (18): 1583–1586. doi:10.1103/PhysRevLett.52.1583. Bibcode: 1984PhRvL..52.1583H. https://link.aps.org/doi/10.1103/PhysRevLett.52.1583. "The appearance of fractional statistics in the present context is strongly reminiscent of the fractional statistics introduced by Wilczek to describe charged particles tied to "magnetic flux tubes" in two dimensions.". 
  46. ↑ 46.0 46.1 Najjar, Dana (May 12, 2020). "'Milestone' Evidence for Anyons, a Third Kingdom of Particles". Wired. https://www.wired.com/story/milestone-evidence-for-anyons-a-third-kingdom-of-particles/. Retrieved September 18, 2020. "In the early 1980s, physicists first used these conditions to observe the 'fractional quantum Hall effect', in which electrons come together to create so-called quasiparticles that have a fraction of the charge of a single electron. (If it seems strange to call the collective behavior of electrons a particle, think of the proton, which is itself made up of three quarks.) In 1984, a seminal two-page paper by Wilczek, Daniel Arovas and John Robert Schrieffer showed that these quasiparticles had to be anyons.". 
  47. ↑ Dumé, Isabelle (May 28, 2020). "Anyons bunch together in a 2D conductor". Physics World. https://physicsworld.com/a/anyons-bunch-together-in-a-2d-conductor/. "The existence of anyons – which get their name from the fact that their behaviour is neither fermion-like or boson-like – was predicted in the early 1980s by the theoretical physicist Frank Wilczek. Soon afterwards, another physicist, Bert Halperin, found that anyons could explain certain aspects of the fractional quantum Hall effect, which describes the changes that take place in electronics at low temperatures in strong magnetic fields. Then, in 1984, Dan Arovas, Bob Schrieffer and Wilczek proved that a successful theory of the fractional quantum Hall effect does indeed require particles that are neither bosons or fermions." 
  48. ↑ Bartolomei, H. (April 10, 2020). "Fractional statistics in anyon collisions". Science 368 (6487): 173–177. doi:10.1126/science.aaz5601. PMID 32273465. Bibcode: 2020Sci...368..173B. https://www.science.org/doi/10.1126/science.aaz5601. 
  49. ↑ Wolchover, Natalie (2013-04-30). "Time Crystals' Could Upend Physicists' Theory of Time". Wired. https://www.wired.com/wiredscience/2013/04/time-crystals/all/. 
  50. ↑ Ball, Phillip (July 17, 2018). "In Search of Time Crystals". Physics World. https://physicsworld.com/a/in-search-of-time-crystals/. ""We discovered experimentally that discrete time crystals not only exist, but that this phase is also remarkably robust." Mikhail Lukin, Harvard University" 
  51. ↑ Woo, Marcus (September 2018). "'Quantum Atmospheres' May Reveal Secrets of Matter" (in en). Quanta Magazine. https://www.quantamagazine.org/quantum-atmospheres-may-reveal-secrets-of-matter-20180925/. 
  52. ↑ Jiang, Qing-Dong; Wilczek, Frank (10 May 2019). "Quantum atmospherics for materials diagnosis". Physical Review B 99 (20): 201104. doi:10.1103/PhysRevB.99.201104. Bibcode: 2019PhRvB..99t1104J. 
  53. ↑ Wilczek, F.; Linder, E. V.; Good, M.R.R. (2020). "Moving mirror model for quasithermal radiation fields". Physical Review D 101 (2): 025012. doi:10.1103/PhysRevD.101.025012. Bibcode: 2020PhRvD.101b5012G. 
  54. ↑ Rokhsar, Daniel S. (1992). "Review of Fractional Statistics and Anyon Superconductivity by Frank Wilczek". Physics Today 45 (2): 101. doi:10.1063/1.2809542. Bibcode: 1992PhT....45b.101W. 

External links



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