1932

Abstract

Driven by breakthroughs in experimental and theoretical techniques, the study of nonequilibrium quantum physics is a rapidly expanding field with many exciting new developments. Among the manifold ways the topic can be investigated, one-dimensional systems provide a particularly fine platform. The trifecta of strongly correlated physics, powerful theoretical techniques, and experimental viability have resulted in a flurry of research activity over the past decade or so. In this review, we explore the nonequilibrium aspects of one-dimensional systems that are integrable. Through a number of illustrative examples, we discuss nonequilibrium phenomena that arise in such models, the role played by integrability, and the consequences these have for more generic systems.

Loading

Article metrics loading...

/content/journals/10.1146/annurev-conmatphys-031119-050630
2020-03-10
2024-06-15
Loading full text...

Full text loading...

/deliver/fulltext/conmatphys/11/1/annurev-conmatphys-031119-050630.html?itemId=/content/journals/10.1146/annurev-conmatphys-031119-050630&mimeType=html&fmt=ahah

Literature Cited

  1. 1. 
    Bloch I, Dalibard J, Zwerger W 2008. Rev. Mod. Phys. 80:885–964
    [Google Scholar]
  2. 2. 
    Schneider C, Porras D, Schaetz T 2012. Rep. Prog. Phys. 75:024401
    [Google Scholar]
  3. 3. 
    Wilson KG. 1975. Rev. Mod. Phys. 47:773–840
    [Google Scholar]
  4. 4. 
    Francesco P, Mathieu P, Sénéchal D 1997. Conformal Field Theory New York: Springer-Verlag
    [Google Scholar]
  5. 5. 
    White SR. 1992. Phys. Rev. Lett. 69:2863–66
    [Google Scholar]
  6. 6. 
    Arnold VI. 1978. Mathematical Methods of Classical Mechanics New York: Spring Sci. Bus. Media
    [Google Scholar]
  7. 7. 
    Bethe H. 1931. Z. Phys. 71:205–26
    [Google Scholar]
  8. 8. 
    Orbach R. 1958. Phys. Rev. 112:309–16
    [Google Scholar]
  9. 9. 
    Yang CN, Yang CP. 1966. Phys. Rev. 150:327–39
    [Google Scholar]
  10. 10. 
    Gaudin M. 1983. The Bethe Wavefunction Cambridge, UK: Cambridge Univ. Press. Trans. J-S Caux, 2014, from French
    [Google Scholar]
  11. 11. 
    Yang CN. 1967. Phys. Rev. Lett. 19:1312–15
    [Google Scholar]
  12. 12. 
    Korepin VE, Bogoliubov NM, Izergin AG 1993. Quantum Inverse Scattering Method and Correlation Functions Cambridge, UK: Cambridge Univ. Press
    [Google Scholar]
  13. 13. 
    Sutherland B. 2004. Beautiful Models: 70 Years of Exactly Solved Quantum Many-Body Problems New Jersey: World Sci.
    [Google Scholar]
  14. 14. 
    Samaj L, Bajnok Z. 2013. Introduction to the Statistical Physics of Integrable Many-Body Systems Cambridge, UK: Cambridge Univ. Press
    [Google Scholar]
  15. 15. 
    Lieb EH, Liniger W. 1963. Phys. Rev. 130:1605–16
    [Google Scholar]
  16. 16. 
    Lieb EH. 1963. Phys. Rev. 130:1616–24
    [Google Scholar]
  17. 17. 
    Zamolodchikov AB, Zamolodchikov AB. 1979. Ann. Phys. 120:2253–91
    [Google Scholar]
  18. 18. 
    Bergknoff H, Thacker HB. 1979. Phys. Rev. D 19:3666–81
    [Google Scholar]
  19. 19. 
    Cazalilla MA, Citro R, Giamarchi T, Orignac E, Rigol M 2011. Rev. Mod. Phys. 83:1405–66
    [Google Scholar]
  20. 20. 
    Guan XW, Batchelor MT, Lee C 2013. Rev. Mod. Phys. 85:1633–91
    [Google Scholar]
  21. 21. 
    Baxter RJ. 1982. Exactly Solved Models in Statistical Mechanics London: Academic
    [Google Scholar]
  22. 22. 
    Lieb EH, Wu FY. 1968. Phys. Rev. Lett. 20:1445–48
    [Google Scholar]
  23. 23. 
    Andrei N, Lowenstein JH. 1980. Phys. Lett. B 91:401–5
    [Google Scholar]
  24. 24. 
    Jaynes ET, Cummings FW. 1963. IEEE Proc 51:89–109
    [Google Scholar]
  25. 25. 
    Andrei N, Furuya K, Lowenstein JH 1983. Rev. Mod. Phys. 55:331–402
    [Google Scholar]
  26. 26. 
    Tsvelick AM, Wiegmann PB. 1983. Adv. Phys. 32:453–713
    [Google Scholar]
  27. 27. 
    Richardson RW. 1968. J. Math. Phys. 9:1327–43
    [Google Scholar]
  28. 28. 
    Dutta O, Gajda M, Hauke P, Lewenstein M, Lhmann DS et al. 2015. Rep. Prog. Phys. 78:066001
    [Google Scholar]
  29. 29. 
    Berges J. 2016. Strongly Interacting Quantum Systems out of Equilibrium: Lecture Notes of the Les Houches Summer School, August 2012, Vol. 99 T Giamarchi, AJ Millis, O Parcollet, H Saleur, LF Cugliandolo 69–206 Oxford, UK: Oxford Univ. Press
    [Google Scholar]
  30. 30. 
    Bertini B, Schuricht D, Essler FHL 2014. J. Stat. Mech.: Theory Exp. 10:10035
    [Google Scholar]
  31. 31. 
    Tang Y, Kao W, Li KY, Seo S, Mallayya K et al. 2018. Phys. Rev. X 8:021030
    [Google Scholar]
  32. 32. 
    Yang CN, Yang CP. 1969. J. Math. Phys. 10:1115–22
    [Google Scholar]
  33. 33. 
    Takahashi M. 1999. Thermodynamics of One-Dimensional Solvable Models Cambridge, UK: Cambridge Univ. Press
    [Google Scholar]
  34. 34. 
    Calabrese P, Cardy J. 2016. J. Stat. Mech.: Theory Exp. 6:064003
    [Google Scholar]
  35. 35. 
    Caux JS, Essler FHL. 2013. Phys. Rev. Lett. 110:257203
    [Google Scholar]
  36. 36. 
    Iyer D, Andrei N. 2012. Phys. Rev. Lett. 109:115304
    [Google Scholar]
  37. 37. 
    James AJA, Konik RM, Lecheminant P, Robinson NJ, Tsvelik AM 2018. Rep. Prog. Phys. 81:046002
    [Google Scholar]
  38. 38. 
    Castro-Alvaredo OA, Doyon B, Yoshimura T 2016. Phys. Rev. X 6:041065
    [Google Scholar]
  39. 39. 
    Bertini B, Collura M, De Nardis J, Fagotti M 2016. Phys. Rev. Lett. 117:207201
    [Google Scholar]
  40. 40. 
    Calabrese P, Cardy J. 2005. J. Stat. Mech.: Theory Exp. 2005:04010
    [Google Scholar]
  41. 41. 
    Calabrese P, Cardy J. 2006. Phys. Rev. Lett. 96:136801
    [Google Scholar]
  42. 42. 
    Mitra A. 2018. Annu. Rev. Condens. Matter Phys. 9:245–59
    [Google Scholar]
  43. 43. 
    N, Iyer D, Guan H 2016. Strongly Interacting Quantum Systems out of Equilibrium: Lecture Notes of the Les Houches Summer School, August 2012, Vol. 99 T Giamarchi, AJ Millis, O Parcollet, H Saleur, LF Cugliandolo 383–418 Oxford, UK: Oxford Univ. Press
    [Google Scholar]
  44. 44. 
    Dóra B, Haque M, Zaránd G 2011. Phys. Rev. Lett. 106:156406
    [Google Scholar]
  45. 45. 
    Smacchia P, Silva A. 2013. Phys. Rev. E 88:042109
    [Google Scholar]
  46. 46. 
    Sharma S, Divakaran U, Polkovnikov A, Dutta A 2016. Phys. Rev. B 93:144306
    [Google Scholar]
  47. 47. 
    Yuzbashyan EA, Altshuler BL, Kuznetsov VB, Enolskii VZ 2005. J. Phys. A Math. Gen. 38:7831–49
    [Google Scholar]
  48. 48. 
    Yuzbashyan EA, Tsyplyatyev O, Altshuler BL 2006. Phys. Rev. Lett. 96:097005
    [Google Scholar]
  49. 49. 
    Yuzbashyan EA, Dzero M. 2006. Phys. Rev. Lett. 96:230404
    [Google Scholar]
  50. 50. 
    Deutsch JM. 1991. Phys. Rev. A 43:2046–49
    [Google Scholar]
  51. 51. 
    Srednicki M. 1994. Phys. Rev. E 50:888–901
    [Google Scholar]
  52. 52. 
    Rigol M, Dunjko V, Olshanii M 2008. Nature 452:854–58
    [Google Scholar]
  53. 53. 
    Cazalilla MA, Chung MC. 2016. J. Stat. Mech.: Theory Exp. 6:064004
    [Google Scholar]
  54. 54. 
    Vidmar L, Rigol M. 2016. J. Stat. Mech.: Theory Exp. 6:064007
    [Google Scholar]
  55. 55. 
    Essler FHL, Fagotti M. 2016. J. Stat. Mech.: Theory Exp. 6:064002
    [Google Scholar]
  56. 56. 
    Caux JS. 2016. J. Stat. Mech.: Theory Exp. 6:064006
    [Google Scholar]
  57. 57. 
    Caux JS, Konik RM. 2012. Phys. Rev. Lett. 109:175301
    [Google Scholar]
  58. 58. 
    Langen T, Erne S, Geiger R, Rauer B, Schweigler T et al. 2015. Science 348:207–11
    [Google Scholar]
  59. 59. 
    Kinoshita T, Wenger T, Weiss DS 2006. Nature 440:900–3
    [Google Scholar]
  60. 60. 
    Gorin T, Prosen T, Seligman TH, Žnidarič M 2006. Phys. Rep 435:33–156
    [Google Scholar]
  61. 61. 
    Heyl M, Polkovnikov A, Kehrein S 2013. Phys. Rev. Lett. 110:135704
    [Google Scholar]
  62. 62. 
    Heyl M. 2018. Rep. Prog. Phys. 81:054001
    [Google Scholar]
  63. 63. 
    Piroli L, Pozsgay B, Vernier E 2018. Nucl. Phys. B 933:454
    [Google Scholar]
  64. 64. 
    Goold J, Plastina F, Gambassi A, Silva A 2018. Thermodynamics in the Quantum Regime: Fundamental Aspects and New Directions F Binder, LA Correa, C Gogolin, J Anders, G Adesso 317–36 Cham, Switz: Springer Nat.
    [Google Scholar]
  65. 65. 
    Talkner P, Lutz E, Hänggi P 2007. Phys. Rev. E 75:050102
    [Google Scholar]
  66. 66. 
    Silva A. 2008. Phys. Rev. Lett. 101:120603
    [Google Scholar]
  67. 67. 
    Türeci HE, Hanl M, Claassen M, Weichselbaum A, Hecht T et al. 2011. Phys. Rev. Lett. 106:107402
    [Google Scholar]
  68. 68. 
    Latta C, Haupt F, Hanl M, Weichselbaum A, Claassen M et al. 2011. Nature 474:627–30
    [Google Scholar]
  69. 69. 
    Dorner R, Clark SR, Heaney L, Fazio R, Goold J, Vedral V 2013. Phys. Rev. Lett. 110:230601
    [Google Scholar]
  70. 70. 
    Cerisola F, Margalit Y, Machluf S, Roncaglia AJ, Paz JP, Folman R 2017. Nat. Commun. 8:1241
    [Google Scholar]
  71. 71. 
    Mahan GD. 2000. Many-Particle Physics New York: Kluwer Acad.
    [Google Scholar]
  72. 72. 
    Sotiriadis S, Gambassi A, Silva A 2013. Phys. Rev. E 87:052129
    [Google Scholar]
  73. 73. 
    Pálmai T, Sotiriadis S. 2014. Phys. Rev. E 90:052102
    [Google Scholar]
  74. 74. 
    Palmai T. 2015. Phys. Rev. B 92:235433
    [Google Scholar]
  75. 75. 
    Rylands C, Andrei N. 2019. Phys. Rev. B 99:085133
    [Google Scholar]
  76. 76. 
    Perfetto G, Piroli L, Gambassi A 2019. arXiv1904.06259
  77. 77. 
    Rylands C, Andrei N. 2019. Phys. Rev. B. 100:064308
    [Google Scholar]
  78. 78. 
    Anderson PW. 1967. Phys. Rev. Lett. 18:1049–51
    [Google Scholar]
  79. 79. 
    Mahan GD. 1967. Phys. Rev. 153:882–89
    [Google Scholar]
  80. 80. 
    Jarzynski C. 1997. Phys. Rev. Lett. 78:2690–93
    [Google Scholar]
  81. 81. 
    Jarzynski C. 2011. Annu. Rev. Condens. Matter Phys. 2:329–51
    [Google Scholar]
  82. 82. 
    Crooks GE. 1999. Phys. Rev. E 60:2721–26
    [Google Scholar]
  83. 83. 
    Heyl M, Kehrein S. 2012. Phys. Rev. Lett. 108:190601
    [Google Scholar]
  84. 84. 
    Korepin VE. 1980. Commun. Math. Phys. 76:165–76
    [Google Scholar]
  85. 85. 
    Brockmann M. 2014. J. Stat. Mech.: Theory Exp. 2014:05006
    [Google Scholar]
  86. 86. 
    De Nardis J, Wouters B, Brockmann M, Caux JS 2014. Phys. Rev. A 89:033601
    [Google Scholar]
  87. 87. 
    Rupasov VI, Iudson VI. 1984. Zhurnal Eksp. Teor. Fiz. 86:819–25
    [Google Scholar]
  88. 88. 
    Goldstein G, Andrei N. 2013. arXiv1309.3471
  89. 89. 
    Iyer D, Guan H, Andrei N 2013. Phys. Rev. A 87:053628
    [Google Scholar]
  90. 90. 
    Hanbury Brown R. 1956. Nature 178:1046–48
    [Google Scholar]
  91. 91. 
    Jeltes T, McNamara JM, Hogervorst W, Vassen W, Krachmalnicoff V et al. 2007. Nature 445:402–5
    [Google Scholar]
  92. 92. 
    Jukić D, Buljan H. 2010. N. J. Phys. 12:055010
    [Google Scholar]
  93. 93. 
    Jukić D, Klajn B, Buljan H 2009. Phys. Rev. A 79:033612
    [Google Scholar]
  94. 94. 
    Jukić D, Pezer R, Gasenzer T, Buljan H 2008. Phys. Rev. A 78:053602
    [Google Scholar]
  95. 95. 
    Preiss PM, Ma R, Tai ME, Lukin A, Rispoli M et al. 2015. Science 347:1229–33
    [Google Scholar]
  96. 96. 
    Weiss DS. 2018. Observation of dynamical fermionization in 1D Bose gases Presented at APS Mar. Meet. 2018 Los Angeles, CA:
    [Google Scholar]
  97. 97. 
    Vasseur R, Trinh K, Haas S, Saleur H 2013. Phys. Rev. Lett. 110:240601
    [Google Scholar]
  98. 98. 
    Kennes DM, Meden V, Vasseur R 2014. Phys. Rev. B 90:115101
    [Google Scholar]
  99. 99. 
    McGuire JB. 1964. J. Math. Phys. 5:622–36
    [Google Scholar]
  100. 100. 
    Piroli L, Calabrese P, Essler FHL 2016. Phys. Rev. Lett. 116:070408
    [Google Scholar]
  101. 101. 
    Piroli L, Calabrese P, Essler FHL 2016. SciPost Phys 1:001
    [Google Scholar]
  102. 102. 
    Zill JC, Wright TM, Kheruntsyan KV, Gasenzer T, Davis MJ 2018. SciPost Phys 4:011
    [Google Scholar]
  103. 103. 
    Yurovsky VA, Malomed BA, Hulet RG, Olshanii M 2017. Phys. Rev. Lett. 119:220401
    [Google Scholar]
  104. 104. 
    Astrakharchik GE, Boronat J, Casulleras J, Giorgini S 2005. Phys. Rev. Lett. 95:190407
    [Google Scholar]
  105. 105. 
    Haller E, Gustavsson M, Mark MJ, Danzl JG, Hart R et al. 2009. Science 325:1224
    [Google Scholar]
  106. 106. 
    Batchelor MT, Bortz M, Guan XW, Oelkers N 2005. J. Stat. Mech.: Theory Exp. 2005:L10001
    [Google Scholar]
  107. 107. 
    Kormos M, Mussardo G, Trombettoni A 2011. Phys. Rev. A 83:013617
    [Google Scholar]
  108. 108. 
    Astrakharchik GE, Blume D, Giorgini S, Granger BE 2004. Phys. Rev. Lett. 92:030402
    [Google Scholar]
  109. 109. 
    Liu W, Andrei N. 2014. Phys. Rev. Lett. 112:257204
    [Google Scholar]
  110. 110. 
    Groha S, Essler FHL. 2017. J. Phys. A Math. Gen. 50:334002
    [Google Scholar]
  111. 111. 
    Fukuhara T, Schauß P, Endres M, Hild S, Cheneau M et al. 2013. Nature 502:76–79
    [Google Scholar]
  112. 112. 
    Fisher MPA, Weichman PB, Grinstein G, Fisher DS 1989. Phys. Rev. B 40:546–70
    [Google Scholar]
  113. 113. 
    Giamarchi T. 2003. Quantum Physics in One Dimension Oxford, UK: Clarendon Press
    [Google Scholar]
  114. 114. 
    Coleman S. 1975. Phys. Rev. D 11:2088–97
    [Google Scholar]
  115. 115. 
    Luther A, Emery VJ. 1974. Phys. Rev. Lett. 33:589–92
    [Google Scholar]
  116. 116. 
    Esposito M, Harbola U, Mukamel S 2009. Rev. Mod. Phys. 81:1665–702
    [Google Scholar]
  117. 117. 
    Iucci A, Cazalilla MA. 2010. N. J. Phys. 12:055019
    [Google Scholar]
  118. 118. 
    Destri C, de Vega HJ 1992. Phys. Rev. Lett. 69:2313–17
    [Google Scholar]
  119. 119. 
    Andraschko F, Sirker J. 2014. Phys. Rev. B 89:125120
    [Google Scholar]
  120. 120. 
    Pozsgay B. 2013. J. Stat. Mech.: Theory Exp. 10:10028
    [Google Scholar]
  121. 121. 
    Piroli L, Pozsgay B, Vernier E 2017. J. Stat. Mech.: Theory Exp. 2:023106
    [Google Scholar]
  122. 122. 
    Piroli L, Pozsgay B, Vernier E 2017. Nuclear Phys. B 925:362–402
    [Google Scholar]
  123. 123. 
    Guan H, Andrei N. 2018. arXiv1803.04846
  124. 124. 
    Fulde P, Ferrell RA. 1964. Phys. Rev. 135:A550–63
    [Google Scholar]
  125. 125. 
    Larkin AI, Ovchinnikov YN. 1964. Zh. Eksp. Teor. Fiz. 47:1136–146 [Sov. Phys. JETP 20,762 (1965)]
    [Google Scholar]
  126. 126. 
    Culver AB, Andrei N. 2019. Submitted. arXiv:1912.02956
  127. 127. 
    Culver AB, Andrei N. 2019. Submitted. arXiv:1912.02172
  128. 128. 
    Bulchandani VB, Vasseur R, Karrasch C, Moore JE 2018. Phys. Rev. B 97:045407
    [Google Scholar]
  129. 129. 
    Bulchandani VB, Vasseur R, Karrasch C, Moore JE 2017. Phys. Rev. Lett. 119:220604
    [Google Scholar]
  130. 130. 
    Doyon B, Yoshimura T. 2017. SciPost Phys 2:014
    [Google Scholar]
/content/journals/10.1146/annurev-conmatphys-031119-050630
Loading
/content/journals/10.1146/annurev-conmatphys-031119-050630
Loading

Data & Media loading...

  • Article Type: Review Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error