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Reviews of topical problems


BCS—BEC crossover, collective excitations, and hydrodynamics of superfluid quantum fluids and gases

 a, b,  c, d
a Kapitza Institute of Physical Problems, Russian Academy of Sciences, ul. Kosygina 2, Moscow, 117334, Russian Federation
b HSE University, ul. Myasnitskaya 20, Moscow, 101000, Russian Federation
c Federal Research Center A.V. Gaponov-Grekhov Institute of Applied Physics of the Russian Academy of Sciences, ul. Ulyanova 46, Nizhny Novgorod, 603000, Russian Federation
d N.I. Lobachevskii Nizhnii Novgorod State University, prosp. Gagarina 23, Nizhnii Novgorod, Russian Federation

A Fermi gas described within the Bardeen—Cooper—Schrieffer theory (BCS) may be converted into a Bose—Einstein condensate (BEC) of composite molecules (dimers) by adiabatically tuning interaction. The sequence of the states that emerges in the process of such a conversion is referred to as the BCS—BEC crossover. We review here the theoretical and experimental results obtained for the BCS—BEC crossover in three- and quasi-two-dimensional quantum gases in the limiting geometry of traps and on optical lattices. We discuss nontrivial phenomena in the hydrodynamics of the superfluid quantum gases and fluids including the collective excitation spectrum in the BCS—BEC crossover, hydrodynamics of the rotating Bose condensates containing a large number of quantized vortices, and the involved and yet unresolved problem of the chiral anomaly in the hydrodynamics of superfluid Fermi systems with an anisotropic p-wave pairing. We also analyze spin-imbalanced quantum gases and the possibilities to realize the triplet p-wave pairing via the Kohn—Luttinger mechanism in those gases. Recent results on two-dimensional Fermi-gas preparation and observation of the fluctuational phenomena related to the Berezinskii—Kosterlitz—Thouless transition in those gases are also reviewed. We briefly discuss the recent experimental discovery of the BCS—BEC crossover and anomalous superconductivity in bilayer graphene and the role of graphene, other Dirac semimetals (such as, for example, bismuth), and 2D optical lattices as potential reference systems that exhibit all of the effects reviewed here.

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Fulltext is also available at DOI: 10.3367/UFNe.2018.10.038471
Keywords: BCS-BEC crossover, hydrodynamics of superfluid quantum fluids and gases, Feshbach resonance, composite fermions and bosons, rotating Bose condensates, chiral anomaly, fermion Goldstone mode, collective excitation spectrum, imbalanced Fermi gas, anomalous pairing, Kohn-Luttinger mechanism, Berezinskii-Kosterlitz-Thouless transition, bilayer graphene
PACS: 03.75.Hh, 67.10.−j, 74.20.−z, 74.25.Uv (all)
DOI: 10.3367/UFNe.2018.10.038471
URL: https://ufn.ru/en/articles/2019/3/a/
000469214700001
2-s2.0-85070731309
2019PhyU...62..215K
Citation: Kagan M Yu, Turlapov A V "BCS—BEC crossover, collective excitations, and hydrodynamics of superfluid quantum fluids and gases" Phys. Usp. 62 215–248 (2019)
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Received: 18th, January 2018, revised: 3rd, October 2018, 31st, October 2018

Оригинал: Каган М Ю, Турлапов А В «Кроссовер БКШ—БЭК, коллективные возбуждения и гидродинамика сверхтекучих квантовых жидкостей и газов» УФН 189 225–261 (2019); DOI: 10.3367/UFNr.2018.10.038471

References (344) ↓ Cited by (24) Similar articles (20)

  1. Anderson M H et al Science 269 198 (1995)
  2. Giorgini S, Pitaevskii L P, Stringari S Rev. Mod. Phys. 80 1215 (2008)
  3. Bloch I, Dalibard J, Zwerger W Rev. Mod. Phys. 80 885 (2008)
  4. Bardeen J, Cooper L N, Schrieffer J R Phys. Rev. 108 1175 (1957)
  5. Schrieffer J R Theory Of Superconductivity (New York: W.A. Benjamin, 1964); Per. na russk. yaz., Shriffer Dzh Teoriya Sverkhprovodimosti (M.: Nauka, 1970)
  6. Cooper L N Phys. Rev. 104 1189 (1956)
  7. Einstein A Sitzungsber. Preuß. Akad. Wiss. Physi.-Math. Kl. 3 (1925)
  8. Eagles D M Phys. Rev. 186 456 (1969)
  9. Leggett A J Modern Trends In The Theory Of Condensed Matter. Proc. Of The XVI Karpacz Winter School Of Theoretical Physics, February 19 - March 3, 1979 Karpacz, Poland (Lecture Notes in Physics) Vol. 115 (Eds A Pekalski, J A Przystawa) (Berlin: Springer-Verlag, 1980) p. 13
  10. Nozières P, Schmitt-Rink S J. Low Temp. Phys. 59 195 (1985)
  11. Keldysh L V, Kozlov A N Zh. Eksp. Teor. Fiz. 54 978 (1968); Keldysh L V, Kozlov A N Sov. Phys. JETP 27 521 (1968)
  12. Gor’kov L P, Melik-Barkhudarov T K Zh. Eksp. Teor. Fiz. 40 1452 (1961); Gor’kov L P, Melik-Barkhudarov T K Sov. Phys. JETP 13 1018 (1961)
  13. Landau L D, Lifshits E M Gidrodinamika 4-e Izd. (M.: Nauka, 1988); Per. na angl. yaz., Landau L D, Lifshitz E M Fluid Mechanics (Oxford: Pergamon Press, 1987)
  14. Landau L D Zh. Eksp. Teor. Fiz. 11 592 (1941); Landau L J. Phys. USSR 5 71 (1941)
  15. Putterman S J Superfluid Hydrodynamics (Amsterdam: North-Holland, 1974); Per. na russk. yaz., Patterman S Gidrodinamika Sverkhtekuchei Zhidkosti (M.: Mir, 1978)
  16. Khalatnikov I M Teoriya Sverkhtekuchesti (M.: Nauka, 1971)
  17. Tilley D R, Tilley J Superfluidity And Superconductivity (New York: Wiley, 1974); Per. na russk. yaz., Tilli D R, Tilli Dzh Sverkhtekuchest’ i Sverkhprovodimost’ (M.: Mir, 1977)
  18. Kagan M Yu Modern Trends In Superconductivity And Superfluidity (Lecture Notes in Physics) Vol. 874 (Dordrecht: Springer, 2013)
  19. Combescot R, Leyronas X, Kagan M Yu Phys. Rev. A 73 023618 (2006)
  20. Kagan M Yu, Frésard R, Capezzali M, Beck H Phys. Rev. B 57 5995 (1998)
  21. Turlapov A V, Kagan M Yu J. Phys. Condens. Matter 29 383004 (2017)
  22. Barmashova T V, Mart’yanov K A, Makhalov V B, Turlapov A V Usp. Fiz. Nauk 186 183 (2016); Barmashova T V, Martiyanov K A, Makhalov V B, Turlapov A V Phys. Usp. 59 174 (2016)
  23. Feshbach H Ann. Physics 19 287 (1962)
  24. Combescot R, Kagan M Yu, Stringari S Phys. Rev. A 74 042717 (2006)
  25. Kagan M Yu, Efremov D V Zh. Eksp. Teor. Fiz. 137 483 (2010); Kagan M Yu, Efremov D V JETP 110 426 (2010)
  26. Kinast J, Turlapov A, Thomas J E Phys. Rev. A 70 051401(R) (2004)
  27. Joseph J et al Phys. Rev. Lett. 98 170401 (2007)
  28. Lifshits E M, Pitaevskii L P Statisticheskaya Fizika Ch. 2 Teoriya Kondensirovannogo Sostoyaniya 3-e izd. (M.: Fizmatlit, 2004); Per. na angl. yaz., Lifshitz E M, Pitaevskii L P Statistical Physics Vol. 2 Theory Of The Condensed State (Oxford: Pegramon Press, 1980)
  29. Kagan M Yu et al Phys. Rev. A 70 023607 (2004)
  30. Kagan M Yu, Efremov D V Phys. Rev. B 65 195103 (2002)
  31. Brodsky I V et al Pis’ma ZhETF 82 306 (2005); Brodsky I V et al JETP Lett. 82 273 (2005)
  32. Brodsky I V et al Phys. Rev. A 73 032724 (2006)
  33. Kagan M Yu i dr Usp. Fiz. Nauk 176 1105 (2006); Kagan M Yu et al Phys. Usp. 49 1079 (2006)
  34. Menushenkov A P, Klement’ev K V, Kuznetsov A V, Kagan M Yu Zh. Eksp. Teor. Fiz. 120 700 (2001); Menushenkov A P, Klementev K V, Kuznetsov A V, Kagan M Yu JETP 93 615 (2001)
  35. Menushenkov A P, Kuznetsov A V, Klementiev K V, Kagan M Yu J. Supercond. Nov. Magn. 29 701 (2016)
  36. Andreev A F, Kagan M Yu Zh. Eksp. Teor. Fiz. 86 546 (1984); Andreev A F, Kagan M Yu Sov. Phys. JETP 59 318 (1984)
  37. Feynman R P Prog. Low Temp. Phys. 1 17 (1955)
  38. Feynman R P Statistical Mechanics: A Set Of Lectures (Boulder: Westview Press, 1998); Per. na russk. yaz., Feinman R Statisticheskaya Mekhanika. Kurs Lektsii (M.: Platon, 2000)
  39. Onsager L Nuovo Cimento 6 ((Suppl. 2)) 249 (1949)
  40. Bekarevich I L, Khalatnikov I M Zh. Eksp. Teor. Fiz. 40 920 (1961); Bekarevich I L, Khalatnikov I M Sov. Phys. JETP 13 643 (1962)
  41. Andronikashvili E L, Mamaladze Yu G Rev. Mod. Phys. 38 567 (1966)
  42. Sonin E B Rev. Mod. Phys. 59 87 (1987)
  43. Baym G, Chandler E J. Low Temp. Phys. 50 57 (1983)
  44. Andronikashvili E L Zh. Eksp. Teor. Fiz. 18 424 (1948)
  45. <?twb=.5w>Volovik G E, Dotsenko V S (ml.). Zh. Eksp. Teor. Fiz. 78 132 (1980); Volovik G E, Dotsenko V S (Jr.) Sov. Phys. JETP 51 65 (1980)
  46. Dzyaloshinskii I E, Volovick G E Ann. Physics 125 67 (1980)
  47. Tkachenko V K Zh. Eksp. Teor. Fiz. 49 1875 (1966); Tkachenko V K Sov. Phys. JETP 22 1282 (1966)
  48. Tkachenko V K Zh. Eksp. Teor. Fiz. 50 1573 (1966); Tkachenko V K Sov. Phys. JETP 23 1049 (1966)
  49. Thomson W (Lord Kelvin) Phil. Mag. 10 155 (1880)
  50. Volovik G E The Universe In Helium Droplet (Oxford: Oxford Univ. Press, 2002)
  51. Vollhardt D, Woelfle P The Superfluid Phases Of Helium 3 (London: Taylor and Francis, 1990)
  52. Andreev A F, Kagan M Yu Zh. Eksp. Teor. Fiz. 93 895 (1987); Andreev A F, Kagan M Yu Sov. Phys. JETP 66 504 (1987)
  53. Balatskii A V, Volovik G E, Konyshev G A Zh. Eksp. Teor. Fiz. 90 2038 (1986); Balatskii A V, Volovik G E, Konyshev G A Sov. Phys. JETP 63 1194 (1986)
  54. Adler S L Phys. Rev. 177 2426 (1969)
  55. Bell J S, Jackiw R Nuovo Cimento A 60 47 (1969)
  56. Jackiw P Lectures On Current Algebra And Its Applications (Princeton, NJ: Princeton Univ. Press, 1972)
  57. Kagan M Y, Efremov D V J. Low Temp. Phys. 158 749 (2010)
  58. Volovik G E Pis’ma ZhETF 98 848 (2013); Volovik G E JETP Lett. 98 753 (2013)
  59. Volovik G E Pis’ma ZhETF 103 147 (2016); Volovik G E JETP Lett. 103 140 (2016)
  60. de Gennes P G Superconductivity Of Metals And Alloys (New York: W.A. Benjamin, 1966); Per. na russk. yaz., De Zhen P Sverkhprovodimost’ Metallov i Splavov (M.: Mir, 1968)
  61. Bogolyubov N N, Tolmachev V V, Shirkov D V Novyi Metod v Teorii Sverkhprovodimosti (M.: Izd-vo AN SSSR, 1958); Per. na angl. yaz., Bogoliubov N N, Tolmachev V V, Shirkov D V A New Method In The Theory Of Superconductivity (New York: Consultants Bureau, 1959)
  62. de Gennes P G The Physics Of Liquid Crystals (Oxford: Clarendon Press, 1974); Per. na russk. yaz., De Zhen P Fizika Zhidkikh Kristallov (M.: Mir, 1977)
  63. Berestetskii V B, Lifshits E M, Pitaevskii L P Kvantovaya Elektrodinamika (M.: Nauka, 1980)
  64. Kohn W, Luttinger J M Phys. Rev. Lett. 15 524 (1965)
  65. Fay D, Layzer A Phys. Rev. Lett. 20 187 (1968)
  66. Kagan M Yu, Chubukov A V Pis’ma ZhETF 47 525 (1988); Kagan M Yu, Chubukov A V JETP Lett. 47 614 (1988)
  67. Kagan M Yu, Chubukov A V Pis’ma ZhETF 50 483 (1989); Kagan M Yu, Chubukov A V JETP Lett. 50 517 (1989)
  68. Kagan M Yu Usp. Fiz. Nauk 164 77 (1994); Kagan M Yu Phys. Usp. 37 69 (1994)
  69. Baranov M A, Kagan M Yu, Kagan Yu Pis’ma ZhETF 64 273 (1996); Baranov M A, Kagan Yu, Kagan M Yu JETP Lett. 64 301 (1996)
  70. Larkin A I, Ovchinnikov Yu N Zh. Eksp. Teor. Fiz. 47 1136 (1964); Larkin A I, Ovchinnikov Yu N Sov. Phys. JETP 20 762 (1965)
  71. Fulde P, Ferrell R A Phys. Rev. 135 A550 (1964)
  72. Kagan M Yu, Kugel’ K I Usp. Fiz. Nauk 171 577 (2001); Kagan M Yu, Kugel’ K I Phys. Usp. 44 553 (2001)
  73. Shin Y et al Phys. Rev. Lett. 97 030401 (2006)
  74. Ong W et al Phys. Rev. Lett. 114 110403 (2015)
  75. Mitra D et al Phys. Rev. Lett. 117 093601 (2016)
  76. Berezinskii V L Zh. Eksp. Teor. Fiz. 61 1144 (1971); Berezinskii V L Sov. Phys. JETP 34 610 (1972)
  77. Kosterlitz J M, Thouless D J J. Phys. C 6 1181 (1973)
  78. Fisher D S, Hohenberg P C Phys. Rev. B 37 4936 (1988)
  79. Beasley M R, Mooij J E, Orlando T P Phys. Rev. Lett. 42 1165 (1979)
  80. José J V (Ed.) 40 Years Of Berezinskii—Kosterlitz—Thouless Theory (Singapore: World Scientific, 2013)
  81. Ryzhov V N Usp. Fiz. Nauk 187 125 (2017); Ryzhov V N Phys. Usp. 60 114 (2017)
  82. Ryzhov V N i dr Usp. Fiz. Nauk 187 921 (2017); Ryzhov V N et al Phys. Usp. 60 857 (2017)
  83. Miyake K Prog. Theor. Phys. 69 1794 (1983)
  84. Randeria M, Duan J-M, Shieh L-Y Phys. Rev. Lett. 62 981 (1989)
  85. Schmitt-Rink S, Varma C M, Ruckenstein A E Phys. Rev. Lett. 63 445 (1989)
  86. Tarruell L et al Nature 483 302 (2012)
  87. Kagan M Yu, Mitskan V A, Korovushkin M M Usp. Fiz. Nauk 185 785 (2015); Kagan M Yu, Mitskan V A, Korovushkin M M Phys. Usp. 58 733 (2015)
  88. Kagan M Yu Pis’ma ZhETF 103 822 (2016); Kagan M Yu JETP Lett. 103 728 (2016)
  89. Di Bernardo A et al Nature Commun. 8 14024 (2017)
  90. Cao Y et al Nature 556 43 (2018)
  91. Bradley C C et al Phys. Rev. Lett. 75 1687 (1995)
  92. Davis K B et al Phys. Rev. Lett. 75 3969 (1995)
  93. Ketterle W, Durfee D S, Stamper-Kurn D M Bose—Einstein Condensation In Atomic Gasesn, Proc. of the Intern. School of Physics "Enrico Fermi") Vol. 140 (Eds M Inguscio, S Stringari, C E Wiema (Amsterdam: IOS Press, 1999) p. 67
  94. Greiner M, Regal C A, Jin D S Nature 426 537 (2003)
  95. Jochim S et al Science 302 2101 (2003)
  96. Zwierlein M W et al Phys. Rev. Lett. 91 250401 (2003)
  97. Bourdel T et al Phys. Rev. Lett. 93 050401 (2004)
  98. Ni K-K et al Science 322 231 (2008)
  99. Chin C et al Rev. Mod. Phys. 82 1225 (2010)
  100. Kagan M Yu Fizika Makroskopicheskikh Kvantovykh Sistem. Kurs Lektsii. Seminary (M.: Izd. dom MEI, 2014)
  101. Pitaevskii L P Usp. Fiz. Nauk 178 633 (2008); Pitaevskii L P Phys. Usp. 51 603 (2008)
  102. Landau L D, Lifshits E M Kvantovaya Mekhanika. Nerelyativistskaya Teoriya 5-e izd. (M.: Fizmatlit, 2002); Per. na angl. yaz., Landau L D, Lifshitz E M Quantum Mechanics. Non-Relativistic Theory (Oxford: Pergamon Press, 1977)
  103. Gurarie V, Radzihovsky L Ann. Physics 322 2 (2007)
  104. Alexandrov A, Ranninger J Phys. Rev. B 23 1796 (1981)
  105. Ranninger J, Micnas R, Robaszkiewicz S Ann. Phys. Fr. 13 455 (1988)
  106. Hubbard J Proc. R. Soc. A 276 238 (1963)
  107. Zürn G et al Phys. Rev. Lett. 110 135301 (2013)
  108. Fano U Nuovo Cimento 12 154 (1935)
  109. Fano U Phys. Rev. 124 1866 (1961)
  110. Kagan M Yu, Val’kov V V, Aksenov S V Phys. Rev. B 95 035411 (2017)
  111. Kinast J et al Phys. Rev. Lett. 92 150402 (2004)
  112. Marsiglio F et al Phys. Rev. B 91 054509 (2015)
  113. Petrov D S, Baranov M A, Shlyapnikov G V Phys. Rev. A 67 031601(R) (2003)
  114. Petrov D S, Salomon C, Shlyapnikov G V Phys. Rev. Lett. 93 090404 (2004)
  115. Prokof’ev N, Ruebenacker O, Svistunov B Phys. Rev. Lett. 87 270402 (2001)
  116. Kashurnikov V A, Prokof’ev N V, Svistunov B V Phys. Rev. Lett. 87 120402 (2001)
  117. Ngampruetikorn V, Levinsen J, Parish M M Phys. Rev. Lett. 111 265301 (2013)
  118. Liu X-J, Hu H, Drummond P D Phys. Rev. B 82 054524 (2010)
  119. Barth M, Hofmann J Phys. Rev. A 89 013614 (2014)
  120. Boettcher I et al Phys. Rev. Lett. 116 045303 (2016)
  121. Fenech K et al Phys. Rev. Lett. 116 045302 (2016)
  122. Vogt E et al Phys. Rev. Lett. 108 070404 (2012)
  123. Chien C-C, Levin K Phys. Rev. A 82 013603 (2010)
  124. Bartenstein M et al Phys. Rev. Lett. 92 120401 (2004)
  125. Heiselberg H Phys. Rev. A 63 043606 (2001)
  126. Pieri P, Pisani L, Strinati G C Phys. Rev. B 72 012506 (2005)
  127. Astrakharchik G E et al Phys. Rev. Lett. 93 200404 (2004)
  128. Burovski E et al Phys. Rev. Lett. 96 160402 (2006)
  129. Landau L D, Lifshits E M Statisticheskaya Fizika Vol. 1 5-e izd. (M.: Fizmatlit, 2001); Per. na angl. yaz., Landau L D, Lifshitz E M Statistical Physics Vol. 1 (Oxford: Pergamon Press, 1980)
  130. Onofrio R Usp. Fiz. Nauk 186 1229 (2016); Onofrio R Phys. Usp. 59 1129 (2016)
  131. Kolachevskii N N, Taichenachev A V Kvantovaya Elektronika 47 393 (2017); Kolachevsky N N, Taichenachev A V Quantum Electron. 47 393 (2017)
  132. Martiyanov K, Makhalov V, Turlapov A Phys. Rev. Lett. 105 030404 (2010)
  133. Fröhlich B et al Phys. Rev. Lett. 106 105301 (2011)
  134. Dyke P et al Phys. Rev. Lett. 106 105304 (2011)
  135. Ando T, Fowler A B, Stern F Rev. Mod. Phys. 54 437 (1982)
  136. Dolgopolov V T Usp. Fiz. Nauk 184 113 (2014); Dolgopolov V T Phys. Usp. 57 105 (2014)
  137. Alikacem N, Sprague D T, Hallock R B Phys. Rev. Lett. 67 2501 (1991)
  138. Saunders J, Lusher C P, Cowan B P Phys. Rev. Lett. 64 2523 (1990)
  139. Østgaard E, Bashkin E P Physica B 178 134 (1992)
  140. Andreev A F Zh. Eksp. Teor. Fiz. 50 1415 (1966); Andreev A F Sov. Phys. JETP 23 939 (1966)
  141. Pavloff N, Treiner J J. Low Temp. Phys. 83 331 (1991)
  142. Dalfovo F, Stringari S Phys. Scripta 38 204 (1988)
  143. Kurihara S J. Phys. Soc. Jpn. 52 1311 (1983)
  144. Novoselov K S et al Science 306 666 (2004)
  145. Kotov V N et al Rev. Mod. Phys. 84 1067 (2012)
  146. Castro Neto A H et al Rev. Mod. Phys. 81 109 (2009)
  147. van der Marel D, van Mechelen J L M, Mazin I I Phys. Rev. B 84 205111 (2011)
  148. Smink A E M et al Phys. Rev. Lett. 118 106401 (2017)
  149. Kagan M Yu et al Solid State Commun. 188 61 (2014)
  150. Hueck K et al Phys. Rev. Lett. 120 060402 (2018)
  151. Feld M et al Nature 480 75 (2011)
  152. Savard T A, O’Hara K M, Thomas J E Phys. Rev. A 56 R1095 (1997)
  153. Gehm M E et al Phys. Rev. A 58 3914 (1998)
  154. Makhalov V, Martiyanov K, Turlapov A Phys. Rev. Lett. 112 045301 (2014)
  155. Dyke P et al Phys. Rev. A 93 011603(R) (2016)
  156. Martiyanov K, Barmashova T, Makhalov V, Turlapov A Phys. Rev. A 93 063622 (2016)
  157. Cheng C et al Phys. Rev. A 94 031606(R) (2016)
  158. Murthy P A et al Phys. Rev. A 90 043611 (2014)
  159. Orel A A et al New J. Phys. 13 113032 (2011)
  160. Mulkerin B C et al Phys. Rev. A 96 053608 (2017)
  161. Salasnich L, Toigo F Phys. Rev. A 91 011604(R) (2015)
  162. He L et al Phys. Rev. A 92 023620 (2015)
  163. Salasnich L, Bighin G J. Supercond. Nov. Magn. 29 3103 (2016)
  164. Murthy P A et al Phys. Rev. Lett. 115 010401 (2015)
  165. Hadzibabic Z et al Nature 441 1118 (2006)
  166. Wu C-T et al Phys. Rev. Lett. 115 240401 (2015)
  167. Choi J, Seo S W, Shin Y Phys. Rev. Lett. 110 175302 (2013)
  168. Boettcher I, Holzmann M Phys. Rev. A 94 011602(R) (2015)
  169. Loktev V M, Quick R M, Sharapov S G Phys. Rep. 349 1 (2001)
  170. Galitskii V M Zh. Eksp. Teor. Fiz. 34 151 (1958); Galitskii V M Sov. Phys. JETP 7 104 (1958)
  171. Bloom P Phys. Rev. B 12 125 (1975)
  172. Josephson B D Phys. Lett. 1 251 (1962)
  173. Josephson B D Adv. Phys. 14 419 (1965)
  174. Baranov M A, Efremov D V, Kagan M Yu Physica C 218 75 (1993)
  175. Laughlin R B Phys. Rev. Lett. 60 2677 (1988)
  176. Fetter A L, Hanna C B, Laughlin R B Phys. Rev. B 39 9679(R) (1989)
  177. Bulaevskii L N, Nagaev E L, Khomskii D I Zh. Eksp. Teor. Fiz. 54 1562 (1968); Bulaevskii L N, Nagaev E L, Khomskii D I Sov. Phys. JETP 27 836 (1968)
  178. Brinkman W F, Rice T M Phys. Rev. B 2 1324 (1970)
  179. Anderson P W Science 235 1196 (1987)
  180. Fulde P Electron Correlations In Molecules And Solids (Springer Series in Solid-State Sciences) Vol. 100 (Berlin: Springer, 1993)
  181. Belinicher V I, Chernyshev A L, Shubin V A Phys. Rev. B 56 3381 (1997)
  182. Shraiman B I, Siggia E D Phys. Rev. B 42 2485 (1990)
  183. Uemura Y J et al Phys. Rev. Lett. 66 2665 (1991)
  184. Kagan M Yu, Rice T M J. Phys. Condens. Matter 6 3771 (1994)
  185. Plakida N M i dr Zh. Eksp. Teor. Fiz. 124 367 (2003); Plakida N M et al JETP 97 331 (2003)
  186. Castellani C, Di Castro C, Grilli M Phys. Rev. Lett. 75 4650 (1995)
  187. Sachdev S Phys. Status Solidi B 247 537 (2010)
  188. Petrov D S, Salomon C, Shlyapnikov G V Phys. Rev. A 71 012708 (2005)
  189. Efimov V I Yad. Fiz. 12 1080 (1970); Efimov V I Sov. J. Nucl. Phys. 12 589 (1971)
  190. Efimov V Phys. Rev. C 44 2303 (1991)
  191. Jensen A S et al Rev. Mod. Phys. 76 215 (2004)
  192. Skornyakov G V, Ter-Martirosyan K A Zh. Eksp. Teor. Fiz. 31 775 (1957); Skorniakov G V, Ter-Martirosian K A Sov. Phys. JETP 4 648 (1957)
  193. Nielsen E et al Phys. Rep. 347 373 (2001)
  194. Nielsen E, Fedorov D V, Jensen A S Few-Body Syst. 27 15 (1999)
  195. Pieri P, Strinati G C Phys. Rev. B 61 15370 (2000)
  196. Bruch L W, Tjon J A Phys. Rev. A 19 425 (1979)
  197. Bardeen J, Baym G, Pines D Phys. Rev. 156 207 (1967)
  198. Bashkin E P, Meyerovich A E Adv. Phys. 30 1 (1981)
  199. Leggett A J Rev. Mod. Phys. 47 331 (1975)
  200. Anderson P W, Morel P Phys. Rev. 123 1911 (1961)
  201. Brinkman W F, Anderson P W Phys. Rev. A 8 2732 (1973)
  202. Brinkman W F, Serene J W, Anderson P W Phys. Rev. A 10 2386 (1974)
  203. Rainer D, Serene J W Phys. Rev. B 13 4745 (1976)
  204. van de Haar P G, Frossati G, Bedell K S J. Low Temp. Phys. 77 (1) 35 (1989)
  205. Kohn W Phys. Rev. Lett. 2 393 (1959)
  206. Friedel J Adv. Phys. 3 446 (1954)
  207. Noz’er F, chastnoe soobshchenie
  208. Efremov D V, Mar’enko M S, Baranov M A, Kagan M Yu Zh. Eksp. Teor. Fiz. 117 990 (2000); Efremov D V, Mar’enko M S, Baranov M A, Kagan M Yu JETP 90 861 (2000)
  209. Kagan M Yu Phys. Lett. A 152 303 (1991)
  210. Frossati G et al Czech. J. Phys. 40 909 (1990)
  211. Wiegers S A J et al Physica B 165-166 733 (1990)
  212. Meierovich A E Pis’ma ZhETF 37 28 (1983); Meyerovich A E JETP Lett. 37 32 (1983)
  213. Roobol L P et al Europhys. Lett. 17 219 (1992)
  214. Castaing B, Noziùres P J. Phys. France 40 257 (1979)
  215. Bashkin E P Zh. Eksp. Teor. Fiz. 78 360 (1980); Bashkin E P Sov. Phys. JETP 51 181 (1980)
  216. Saunders J et al Physica B 280 100 (2000)
  217. Morley G W et al J. Low Temp. Phys. 126 557 (2002)
  218. Efremov D V, Viverit L Phys. Rev. B 65 134519 (2002)
  219. Roati G et al Phys. Rev. Lett. 89 150403 (2002)
  220. Modugno G et al Science 297 2240 (2002)
  221. Stoof H T C et al Phys. Rev. Lett. 76 10 (1996)
  222. Migdal A B Kachestvennye Metody v Kvantovoi Teorii (M.: Nauka, 1975); Migdal A B Qualitative Methods In Quantum Theory (Cambridge, Mass.: Advanced Book Program, 2000)
  223. Kagan M Yu, Val’kov V V Zh. Eksp. Teor. Fiz. 140 179 (2011); Kagan M Yu, Val’kov V V JETP 113 156 (2011)
  224. Kagan M Y, Val’kov V V J. Supercond. Nov. Magn. 25 1379 (2012)
  225. Baranov M A, Chubukov A V, Kagan M Yu Int. J. Mod. Phys. B 06 2471 (1992)
  226. Baranov M A, Kagan M Yu Zh. Eksp. Teor. Fiz. 102 313 (1992); Baranov M A, Kagan M Y JETP 75 165 (1992)
  227. Liao Y et al Nature 467 567 (2010)
  228. Shin Y et al Nature 451 689 (2008)
  229. Cladé P et al Phys. Rev. Lett. 102 170401 (2009)
  230. Inada Y et al Phys. Rev. Lett. 101 100401 (2008)
  231. Fuchs J et al Phys. Rev. A 77 053616 (2008)
  232. Gaebler J P et al Phys. Rev. Lett. 98 200403 (2007)
  233. Littlewood P B, Varelogiannes G (Eds) Proc. Of The First EuroConf. On Anomalous Complex Superconductors, Crete, Greece, September 1998 (Amstedam: North-Holland, 1999)
  234. Hertz J A Phys. Rev. B 14 1165 (1976)
  235. Millis A J Phys. Rev. B 48 7183 (1993)
  236. Kagan M Yu, Ogarkov S L Laser Phys. 18 509 (2008)
  237. Read N, Green D Phys. Rev. B 61 10267 (2000)
  238. Iskin M, Sá de Melo C A R Phys. Rev. Lett. 96 040402 (2006)
  239. Botelho S, Sá de Melo C A R J. Low Temp. Phys. 140 409 (2005)
  240. Volovik G E, Solov’ev A, Yakovenko V M Pis’ma ZhETF 49 55 (1989); Volovik G E, Solov’ev A, Yakovenko V M JETP Lett. 49 65 (1989)
  241. Majorana E Nuovo Cimento 14 171 (1937)
  242. Volovik G E Pis’ma ZhETF 90 440 (2009); Volovik G E JETP Lett. 90 398 (2009)
  243. Bogolyubov N N Zh. Eksp. Teor. Fiz. 34 58 (1958); Bogoliubov N N JETP 7 41 (1958)
  244. Tolmachev V V, Tyablikov S V Zh. Eksp. Teor. Fiz. 34 66 (1958); Tolmachev V V, Tiablikov S V Sov. Phys. JETP 7 46 (1958)
  245. Bogolyubov N N ZhEFT 34 73 (1958); Bogoliubov N N Sov. Phys. JETP 7 51 (1958)
  246. Anderson P W Phys. Rev. 112 1900 (1958)
  247. Minguzzi A, Ferrari G, Casin Y Eur. Phys. J. D 17 49 (2001)
  248. Büchler H P, Zoller P, Zwerger W Phys. Rev. Lett. 93 080401 (2004)
  249. Pieri P, Pisani L, Strinati G C Phys. Rev. B 70 094508 (2004)
  250. Andrenacci N, Pieri P, Strinati G C Phys. Rev. B 68 144507 (2003)
  251. Kosztin I et al Phys. Rev. B 61 11662 (2000)
  252. Abrikosov A A, Gor’kov L P, Dzyaloshinskii I E Metody Kvantovoi Teorii Polya v Statisticheskoi Fizike (M.: Dobrosvet, 1998); Per. na angl. yaz., Abrikosov A A, Gorkov L P, Dzyaloshinski I E Methods Of Quantum Field Theory In Statistical Physics (New York: Dover Publ., 1975)
  253. Pistolesi F, Strinati G C Phys. Rev. B 53 15168 (1996)
  254. Bartenstein M et al Phys. Rev. Lett. 94 103201 (2005)
  255. Andrews M R et al Phys. Rev. Lett. 79 553 (1997)
  256. Capuzzi P et al Phys. Rev. A 73 021603(R) (2006)
  257. Astrakharchik G E (2006), chastnaya perepiska
  258. Heiselberg H Phys. Rev. A 73 013607 (2006)
  259. Guéry-Odelin D et al Phys. Rev. A 60 4851 (1999)
  260. Baranov M A, Petrov D S Phys. Rev. A 62 041601(R) (2000)
  261. Vichi L J. Low Temp. Phys. 121 177 (2000)
  262. Pedri P, Guéry-Odelin D, Stringari S Phys. Rev. A 68 043608 (2003)
  263. Kim Y E, Zubarev A L Phys. Lett. A 327 397 (2004)
  264. Heiselberg H Phys. Rev. Lett. 93 040402 (2004)
  265. Kim Y E, Zubarev A L Phys. Rev. A 70 033612 (2004)
  266. Heiselberg H New J. Phys. 6 137 (2004)
  267. Hu H et al Phys. Rev. Lett. 93 190403 (2004)
  268. Astrakharchik G E et al Phys. Rev. Lett. 95 030404 (2005)
  269. Bruun G M, Smith H Phys. Rev. A 72 043605 (2005)
  270. Bruun G M, Smith H Phys. Rev. A 75 043612 (2007)
  271. Bartenstein M et al Phys. Rev. Lett. 92 203201 (2004)
  272. Kinast J, Turlapov A, Thomas J E Phys. Rev. Lett. 94 170404 (2005)
  273. Altmeyer A et al Phys. Rev. Lett. 98 040401 (2007)
  274. Kinast J M PhD Thesis (Durham, NC: Duke Univ., 2006)
  275. O’Hara K M et al Science 298 2179 (2002)
  276. Thomas J E, Kinast J, Turlapov A Phys. Rev. Lett. 95 120402 (2005)
  277. Ku M J H et al Science 335 563 (2012)
  278. Lee T D, Yang C N Phys. Rev. 105 1119 (1957)
  279. Lee T D, Huang K, Yang C N Phys. Rev. 106 1135 (1957)
  280. Bevan T D C et al Nature 386 689 (1997)
  281. Dmitriev V V et al Pis’ma ZhETF 86 681 (2007); Dmitriev V V et al JETP Lett. 86 594 (2007)
  282. Mermin N D, Muzikar P Phys. Rev. B 21 980 (1980)
  283. Stone M, Anduaga I Ann. Physics 323 2 (2008)
  284. Vakaryuk V, Leggett A J Phys. Rev. Lett. 103 057003 (2009)
  285. Volovik G E Pis’ma ZhETF 61 935 (1995); Volovik G E JETP Lett. 61 958 (1995)
  286. Volovik G E Pis’ma ZhETF 100 843 (2015); Volovik G E JETP Lett. 100 742 (2015)
  287. Tada Y, Nie W, Oshikawa M Phys. Rev. Lett. 114 195301 (2015)
  288. Shitade A, Nagai Y Phys. Rev. B 93 174517 (2016)
  289. Sauls J A Phys. Rev. B 84 214509 (2011)
  290. Combescot R, Dombre T Phys. Rev. B 33 79 (1986)
  291. Itzykson C, Zuber J-B Quantum Field Theory (New York: McGraw-Hill, 1980); Per. na russk. yaz., Itsikson K, Zyuber Zh-B Kvantovaya Teoriya Polya T. 2 (Novokuznetsk: Novokuznetskii fiz.-mat. institut, 2000)
  292. Akulov V P, Volkov D V Pis’ma ZhETF 17 367 (1973); Akulov V P, Volkov D V JETP Lett. 17 261 (1973)
  293. Cross M C J. Low Temp. Phys. 26 165 (1977)
  294. Kopnin N B, Soininen P I, Salomaa M M Phys. Rev. B 45 5491 (1992)
  295. Kopnin N B, Volovik G E, Parts Ü Europhys. Lett. 32 651 (1995)
  296. Haldane F D M Phys. Rev. Lett. 93 206602 (2004)
  297. Baym G Phys. Rev. A 69 043618 (2004)
  298. Fetter A L Rev. Mod. Phys. 81 647 (2009)
  299. Matveenko S I, Shlyapnikov G V Phys. Rev. A 83 033604 (2011)
  300. Cooper N R Adv. Phys. 57 539 (2008)
  301. Aftalion A, Blanc X, Dalibard J Phys. Rev. A 71 023611 (2005)
  302. Volovik G E Exotic Properties Of Superfluid He-3 (Singapore: World Scientific, 1992)
  303. Simonucci S, Pieri P, Strinati G C Nature Phys. 11 941 (2015)
  304. Mizushima T, Machida K Phys. Rev. A 81 053605 (2010)
  305. Thouless D J, Ao P, Niu Q Phys. Rev. Lett. 76 3758 (1996)
  306. Brusov P N, Brusov P P Collective Excitations In Unconventional Superconductors And Superfluids (New Jersey: World Scientific, 2010)
  307. Chubukov A V Phys. Rev. B 52 R3840 (1995)
  308. Son D T, Spivak B Z Phys. Rev. B 88 104412 (2013)
  309. Spivak B Z, Andreev A V Phys. Rev. B 93 085107 (2016)
  310. Andreev A V, Spivak B Z Phys. Rev. Lett. 120 026601 (2018)
  311. Kim H-J et al Phys. Rev. Lett. 111 246603 (2013)
  312. Shen S-Q, Li C-A, Niu Q 2D Mater. 4 035014 (2017)
  313. Kuntsevich A Yu et al New J. Phys. 20 103022 (2018)
  314. Abrikosov A A Zh. Eksp. Teor. Fiz. 32 1442 (1957); Abrikosov A A Sov. Phys. JETP 5 1174 (1957)
  315. Iordanskii S V Zh. Eksp. Teor. Fiz. 49 225 (1966); Iordanskii S V Sov. Phys. JETP 22 160 (1966)
  316. Hall H E Adv. Phys. 9 (33) 89 (1960)
  317. Hall H E, Vinen W F Proc. R. Soc. A 238 215 (1956)
  318. Cooper N R, Wilkin N K, Gunn J M F Phys. Rev. Lett. 87 120405 (2001)
  319. Cooper N R, Komineas S, Read N Phys. Rev. A 70 033604 (2004)
  320. Gifford S A, Baym G Phys. Rev. A 70 033602 (2004)
  321. Kittel Ch Quantum Theory Of Solids (New York: Wiley, 1963); Per. na russk. yaz., Kittel’ Ch Kvantovaya Teoriya Tverdykh Tel (M.: Nauka, 1967)
  322. Packard R E Physica B+C 109-110 1474 (1982)
  323. Yarmchuk E J, Gordon M J V, Packard R E Phys. Rev. Lett. 43 214 (1979)
  324. Yarmchuk E J, Packard R E J. Low Temp. Phys. 46 479 (1982)
  325. Bretin V et al Phys. Rev. Lett. 92 050403 (2004)
  326. Madison K W et al Phys. Rev. Lett. 84 806 (2000)
  327. Chevy F, Madison K W, Dalibard J Phys. Rev. Lett. 85 2223 (2000)
  328. Madison K W et al Phys. Rev. Lett. 86 4443 (2001)
  329. Abo-Shaeer J R et al Science 292 476 (2001)
  330. Zwierlein M W et al Nature 435 1047 (2005)
  331. Kovtun P K, Son D T, Starinets A O Phys. Rev. Lett. 94 111601 (2005)
  332. Turlapov A et al J. Low Temp. Phys. 150 567 (2008)
  333. Ravenhall D G, Pethick C J, Wilson J R Phys. Rev. Lett. 50 2066 (1983)
  334. Maruyama T et al Phys. Rev. C 72 015802 (2005)
  335. Maruyama T et al Phys. Rev. C 73 035802 (2006)
  336. Pons J A, Viganò D, Rea N Nature Phys. 9 431 (2013)
  337. Kerbikov B Surv. High Energy Phys. 20 47 (2006)
  338. Hwang E H, Das Sarma S Phys. Rev. B 75 205418 (2007)
  339. Laughlin R B Rev. Mod. Phys. 71 863 (1999)
  340. Rezayi E H, Haldane F D M Phys. Rev. B 50 17199 (1994)
  341. Lifshits E M, Pitaevskii L P Fizicheskaya Kinetika 2-e Izd. (M.: Fizmatlit, 2001); Per. na angl. yaz., Lifshitz E M, Pitaevskii L P Physical Kinetics (Oxford: Pergamon Press, 1981)
  342. Bandurin D A et al Science 351 1055 (2016)
  343. Kagan M Yu, Mitskan V A, Korovushkin M M Zh. Eksp. Teor. Fiz. 146 1301 (2014); Kagan M Yu, Mitskan V A, Korovushkin M M JETP 119 1140 (2014)
  344. Lozovik Yu E, Merkulova S P, Sokolik A A Usp. Fiz. Nauk 178 757 (2008); Lozovik Yu E, Merkulova S P, Sokolik A A Phys. Usp. 51 727 (2008)
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