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Colloquium: Nonequilibrium dynamics of closed interacting quantum systems

Anatoli Polkovnikov, Krishnendu Sengupta, Alessandro Silva, and Mukund Vengalattore

Anatoli Polkovnikov

  • Department of Physics, Boston University, Boston, Massachusetts 02215, USA

Krishnendu Sengupta

  • Theoretical Physics Department, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032, India

Alessandro Silva

  • The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy

Mukund Vengalattore

  • Department of Physics, Cornell University, Ithaca, New York 14853, USA

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Rev. Mod. Phys. 83, 863 – Published 15 August, 2011

DOI: https://doi.org/10.1103/RevModPhys.83.863

Abstract

This Colloquium gives an overview of recent theoretical and experimental progress in the area of nonequilibrium dynamics of isolated quantum systems. There is particularly a focus on quantum quenches: the temporal evolution following a sudden or slow change of the coupling constants of the system Hamiltonian. Several aspects of the slow dynamics in driven systems are discussed and the universality of such dynamics in gapless systems with specific focus on dynamics near continuous quantum phase transitions is emphasized. Recent progress on understanding thermalization in closed systems through the eigenstate thermalization hypothesis is also reviewed and relaxation in integrable systems is discussed. Finally key experiments probing quantum dynamics in cold atom systems are overviewed and put into the context of our current theoretical understanding.

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References (226)

  1. Allahverdyan, A. E., and T. M. Nieuwenhuizen, 2002, Physica (Amsterdam) 305A, 542.
  2. Allahverdyan, A. E., and T. M. Nieuwenhuizen, 2005, Phys. Rev. E 71, 046107.
  3. Altland, A., V. Gurarie, T. Kriecherbauer, and A. Polkovnikov, 2009, Phys. Rev. A 79, 042703.
  4. Altshuler, B. L., Y. Gefen, A. Kamenev, and L. S. Levitov, 1997, Phys. Rev. Lett. 78, 2803.
  5. Anderson, P. W., 1958, Phys. Rev. 109, 1492.
  6. Appel, J., P. J. Windpassinger, D. Oblak, U. B. Hoff, N. Kjaergaard, and E. S. Polzik, 2009, Proc. Natl. Acad. Sci. U.S.A. 106, 10 960.
  7. Babadi, M., D. Pekker, R. Sensarma, A. Georges, and E. Demler, 2009, arXiv:0908.3483.
  8. Balian, R., 1991, From Microphysics to Macrophysics (Springer, Berlin).
  9. Barankov, R., and A. Polkovnikov, 2008, Phys. Rev. Lett. 101, 076801.
  10. Barmettler, P., M. Punk, V. Gritsev, E. Demler, and E. Altman, 2009, Phys. Rev. Lett. 102, 130603.
  11. Barouch, E., B. M. McCoy, and M. Dresden, 1970, Phys. Rev. A 2, 1075.
  12. Barthel, T., and U. Schollwöck, 2008, Phys. Rev. Lett. 100, 100601.
  13. Basko, D. M., I. L. Aleiner, and B. L. Altshuler, 2006, Ann. Phys. (N.Y.) 321, 1126.
  14. Bermudez, A., D. Patanè, L. Amico, and M. A. Martin-Delgado, 2009, Phys. Rev. Lett. 102, 135702.
  15. Biroli, G., L. F. Cugliandolo, and A. Sicilia, 2010, Phys. Rev. E 81, 050101.
  16. Blakie, P. B., A. S. Bradley, M. J. Davis, R. J. Ballagh, and C. W. Gardiner, 2008, Adv. Phys. 57, 363.
  17. Bloch, I., J. Dalibard, and W. Zwerger, 2008, Rev. Mod. Phys. 80, 885.
  18. Boksenbojm, E., B. Wynants, and C. Jarzynski, 2010, Physica (Amsterdam) A389, 4406.
  19. Burkov, A. A., M. D. Lukin, and E. Demler, 2007, Phys. Rev. Lett. 98, 200404.
  20. Calabrese, P., and J. Cardy, 2004, J. Stat. Mech., P06002.
  21. Calabrese, P., and J. Cardy, 2005, J. Stat. Mech., P04010.
  22. Calabrese, P., and J. Cardy, 2007, J. Stat. Mech., P06008.
  23. Campbell, D. K., P. Rosenau, and G. Zaslavsky, 2005, Chaos 15, 015101.
  24. Caneva, T., R. Fazio, and G. E. Santoro, 2007, Phys. Rev. B 76, 144427.
  25. Canovi, E., D. Rossini, R. Fazio, G. Santoro, and A. Silva, 2011, Phys. Rev. B 83, 094431.
  26. Cassidy, A. C., C. W. Clark, and M. Rigol, 2011, Phys. Rev. Lett. 106, 140405.
  27. Caux, J.-S., and J. Mossel, 2011, J. Stat. Mech., P02023.
  28. Cazalilla, M. A., 2006, Phys. Rev. Lett. 97, 156403.
  29. Chaikin, P. M., and T. C. Lubensky, 1995, Principles of Condensed Matter Physics (Cambridge University Press, Cambridge, UK).
  30. Chang, D. E., V. Gritsev, G. Morigi, V. Vuletić, M. D. Lukin, and E. A. Demler, 2008, Nature Phys. 4, 884.
  31. Chang, M. S., Q. S. Qin, W. X. Zhang, L. You, and M. S. Chapman, 2005, Nature Phys. 1, 111.
  32. Cherng, R. W., and L. S. Levitov, 2006, Phys. Rev. A 73, 043614.
  33. Chuang, I., R. Durrer, N. Turok, and B. Yurke, 1991, Science 251, 1336.
  34. Cincio, L., J. Dziarmaga, M. M. Rams, and W. H. Zurek, 2007, Phys. Rev. A 75, 052321.
  35. Collura, M., and D. Karevski, 2010, Phys. Rev. Lett. 104, 200601.
  36. Cramer, M., C. M. Dawson, J. Eisert, and T. J. Osborne, 2008, Phys. Rev. Lett. 100, 030602.
  37. Cramer, M., and J. Eisert, 2010, New J. Phys. 12, 055020.
  38. Cucchietti, F. M., B. Damski, J. Dziarmaga, and W. H. Zurek, 2007, Phys. Rev. A 75, 023603.
  39. Damski, B., and W. H. Zurek, 2006, Phys. Rev. A 73, 063405.
  40. De Grandi, C., R. A. Barankov, and A. Polkovnikov, 2008, Phys. Rev. Lett. 101, 230402.
  41. De Grandi, C., V. Gritsev, and A. Polkovnikov, 2010a, Phys. Rev. B 81, 224301.
  42. De Grandi, C., V. Gritsev, and A. Polkovnikov, 2010b, Phys. Rev. B 81, 012303.
  43. De Grandi, C., and A. Polkovnikov, 2010, Lect. Notes Phys. 802, 75.
  44. Deng, S., G. Ortiz, and L. Viola, 2008, Europhys. Lett. 84, 67 008.
  45. Deutsch, J., 1991, Phys. Rev. A 43, 2046.
  46. Divakaran, U., A. Dutta, and D. Sen, 2008, Phys. Rev. B 78, 144301.
  47. Divakaran, U., A. Dutta, and D. Sen, 2010, Phys. Rev. B 81, 054306.
  48. Dóra, B., E. V. Castro, and R. Moessner, 2010, Phys. Rev. B 82, 125441.
  49. Dóra, B., and R. Moessner, 2010, Phys. Rev. B 81, 165431.
  50. Ducci, S., P. L. Ramazza, W. González-Viňas, and F. T. Arecchi, 1999, Phys. Rev. Lett. 83, 5210.
  51. Dziarmaga, J., 2005, Phys. Rev. Lett. 95, 245701.
  52. Dziarmaga, J., 2006, Phys. Rev. B 74, 064416.
  53. Dziarmaga, J., 2010, Adv. Phys. 59, 1063.
  54. Dziarmaga, J., J. Meisner, and W. Zurek, 2008, Phys. Rev. Lett. 101, 115701.
  55. Dziarmaga, J., and M. M. Rams, 2010, New J. Phys. 12, 055007.
  56. Eckstein, M., and M. Kollar, 2008, Phys. Rev. Lett. 100, 120404.
  57. Eckstein, M., and M. Kollar, 2010, New J. Phys. 12, 055012.
  58. Estéve, J., C. Gross, A. Weller, S. Giovanazzi, and M. K. Oberthaler, 2008, Nature (London) 455, 1216.
  59. Farhi, E., J. Goldstone, S. Gutmann, J. Lapan, A. Lundgren, and D. Preda, 2001, Science 292, 472.
  60. Fermi, E., J. Pasta, and S. Ulam, May 1955, Document LA-1940.
  61. Fioretto, D., and G. Mussardo, 2010, New J. Phys. 12, 055015.
  62. Fisher, D. S., 1995, Phys. Rev. B 51, 6411.
  63. Flesch, A., M. Cramer, I. McCulloch, U. Schollwoeck, and J. Eisert, 2008, Phys. Rev. A 78, 033608.
  64. Fubini, A., G. Falci, and A. Osterloh, 2007, New J. Phys. 9, 134.
  65. Gangardt, D. M., and M. Pustilnik, 2008, Phys. Rev. A 77, 041604(R).
  66. Gardiner, C., and P. Zoller, 2004, Quantum Noise (Springer-Verlag, Berlin), 3rd ed.
  67. Gasenzer, T., 2009, Eur. Phys. J. Special Topics 168, 89.
  68. Ghoshal, S., and A. B. Zamolodchikov, 1994, Int. J. Mod. Phys. A 9, 3841.
  69. Girardeau, M. D., 1969, Phys. Lett. 30A, 442.
  70. Girardeau, M. D., 1970, Phys. Lett. 32A, 67.
  71. Gogolin, C., M. P. Müller, and J. Eisert, 2011, Phys. Rev. Lett. 106, 040401.
  72. Goldstein, S., J. L. Lebowitz, R. Tumulka, and N. Zanghi, 2010, Eur. Phys. J. H 35, 173.
  73. Greentree, A. D., C. Tahan, J. H. Cole, and L. C. L. Hollenberg, 2006, Nature Phys. 2, 856.
  74. Greiner, M., O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, 2002a, Nature (London) 415, 39.
  75. Greiner, M., O. Mandel, T. W. Hansch, and I. Bloch, 2002b, Nature (London) 419, 51.
  76. Gritsev, V., E. Demler, E. Lukin, and A. Polkovnikov, 2007, Phys. Rev. Lett. 99, 200404.
  77. Gritsev, V., and A. Polkovnikov, 2010, in Understanding Quantum Phase Transitions, edited by L. Carr (Taylor & Francis, Boca Raton).
  78. Gu, S.-J., and H.-Q. Lin, 2009, Europhys. Lett. 87, 10 003.
  79. Gurarie, V., 1995, Nucl. Phys. B441, 569.
  80. Hillery, M. A., R. F. O’Connell, M. O. Scully, and E. P. Wigner, 1984, Phys. Rep. 106, 121.
  81. Hindmarsh, M., and A. Rajantie, 2000, Phys. Rev. Lett. 85, 4660.
  82. Ho, T. L., 1998, Phys. Rev. Lett. 81, 742.
  83. Hofferberth, S., I. Lesanovsky, B. Fischer, T. Schumm, and J. Schmiedmayer, 2007, Nature (London) 449, 324.
  84. Imry, Y., 1997, Introduction to Mesoscopic Physics (Oxford University Press, New York).
  85. Itin, A., and P. Törmä, 2009a, arXiv:0901.4778.
  86. Itin, A. P., and P. Törmä, 2009b, Phys. Rev. A 79, 055602.
  87. Iucci, A., and M. A. Cazalilla, 2009, Phys. Rev. A 80, 063619.
  88. Izrailev, F. M., and B. V. Chirikov, 1966, Sov. Phys. Dokl. 11, 32.
  89. Jaynes, E., 1957, Phys. Rev. 106, 620.
  90. Jo, G.-B., Y. R. Lee, J.-H. Choi, C. A. Christensen, T. H. Kim, J. H. Thywissen, D. E. Pritchard, and W. Ketterle, 2009, Science 325, 1521.
  91. Kamenev, A., and A. Levchenko, 2009, Adv. Phys. 58, 197.
  92. Kardar, M., 2007, Statistical Physics of Particles (Cambridge University Press, Cambridge, UK).
  93. Kibble, T., 2007, Phys. Today 60, No. 9, 47.
  94. Kibble, T. W. B., 1976, J. Phys. A 9, 1387.
  95. Kiegel, C., 2009, Diploma thesis: Semiclassical approach to driven many-particle systems (Institute for Theoretical Physics, University of Cologne, Germany).
  96. Kinoshita, T., T. Wenger, and D. S. Weiss, 2006, Nature (London) 440, 900.
  97. Klempt, C., O. Topic, G. Gebreyesus, M. Scherer, T. Henninger, P. Hyllus, W. Ertmer, L. Santos, and J. J. Arlt, 2010, Phys. Rev. Lett. 104, 195303.
  98. Klich, I., and L. Levitov, 2009, Phys. Rev. Lett. 102, 100502.
  99. Klich, I., G. Refael, and A. Silva, 2006, Phys. Rev. A 74, 032306.
  100. Kollar, M., and M. Eckstein, 2008, Phys. Rev. A 78, 013626.
  101. Kollath, C., A. M. Läuchli, and E. Altman, 2007, Phys. Rev. Lett. 98, 180601.
  102. Krapivsky, P. L., 2010, J. Stat. Mech., P02014.
  103. Kronjäger, J., C. Becker, M. Brinkmann, R. Walser, P. Navez, K. Bongs, and K. Sengstock, 2005, Phys. Rev. A 72, 063619.
  104. Laguna, P., and W. H. Zurek, 1997, Phys. Rev. Lett. 78, 2519.
  105. Lamacraft, A., 2007, Phys. Rev. Lett. 98, 160404.
  106. Landau, L., 1932, Phys. Z. Sowjetunion 1, 88.
  107. Landau, L., and E. Lifshitz, 1981, Quantum Mechanics: Non-Relativistic Theory (Butterworth-Heinemann, Oxford, UK), Vol. 3.
  108. Landau, L., and E. Lifshitz, 1982, Mechanics: Course of Theoretical Physics (Butterworth-Heinemann, Oxford, UK), Vol. 1.
  109. Landau, L. D., and E. M. Lifshitz, 1980, Statistical Physics (Butterworth-Heinemann, Oxford, UK), 3rd ed., Pt. 1, Vol. 5.
  110. Leitner, D. M., and P. G. Wolynes, 1996, Phys. Rev. Lett. 76, 216.
  111. Leroux, I. D., M. H. Schleier-Smith, and V. Vuletić, 2010, Phys. Rev. Lett. 104, 073602.
  112. Lignier, H., C. Sias, D. Ciampini, Y. Singh, A. Zenesini, O. Morsch, and E. Arimondo, 2007, Phys. Rev. Lett. 99, 220403.
  113. Linden, N., S. Popescu, A. Short, and A. Winter, 2009, Phys. Rev. E 79, 061103.
  114. Logan, D. E., and P. G. Wolynes, 1990, J. Chem. Phys. 93, 4994.
  115. Luo, L., B. Clancy, J. Joseph, J. Kinast, and J. E. Thomas, 2007, Phys. Rev. Lett. 98, 080402.
  116. Majorana, E., 1932, Nuovo Cimento 9, 43.
  117. Maniv, A., E. Polturak, and G. Koren, 2003, Phys. Rev. Lett. 91, 197001.
  118. Manmana, S. R., S. Wessel, R. M. Noack, and A. Muramatsu, 2007, Phys. Rev. Lett. 98, 210405.
  119. Mathey, L., and A. Polkovnikov, 2010, Phys. Rev. A 81, 033605.
  120. Mazur, P., 1969, Physica (Amsterdam) 43, 533.
  121. Meiser, D., J. Ye, and M. J. Holland, 2008, New J. Phys. 10, 073014.
  122. Moeckel, M., and S. Kehrein, 2008, Phys. Rev. Lett. 100, 175702.
  123. Moeckel, M., and S. Kehrein, 2009, Ann. Phys. (N.Y.) 324, 2146.
  124. Moeckel, M., and S. Kehrein, 2010, New J. Phys. 12, 055016.
  125. Monaco, R., M. Aaroe, J. Mygind, R. J. Rivers, and V. P. Koshelets, 2006, Phys. Rev. B 74, 144513.
  126. Monaco, R., J. Mygind, and R. J. Rivers, 2002, Phys. Rev. Lett. 89, 080603.
  127. Monaco, R., J. Mygrind, R. J. Rivers, and V. P. Koshelets, 2009, Phys. Rev. B 80, 180501.
  128. Mondal, S., D. Sen, and K. Sengupta, 2008, Phys. Rev. B 78, 045101.
  129. Mondal, S., K. Sengupta, and D. Sen, 2009, Phys. Rev. B 79, 045128.
  130. Mostame, S., G. Schaller, and R. Schützhold, 2007, Phys. Rev. A 76, 030304(R).
  131. Mukerjee, S., V. Oganesyan, and D. Huse, 2006, Phys. Rev. B 73, 035113.
  132. Mukherjee, V., U. Divakaran, A. Dutta, and D. Sen, 2007, Phys. Rev. B 76, 174303.
  133. Mukherjee, V., A. Dutta, and D. Sen, 2008, Phys. Rev. B 77, 214427.
  134. Mussardo, G., 2009, Statistical Field Theory. An Introduction to Exactly Solved Models in Statistical Physics (Oxford University Press, New York).
  135. Neuenhahn, C., and F. Marquardt, 2010, arXiv:1007.5306.
  136. Oganesyan, V., and D. A. Huse, 2007, Phys. Rev. B 75, 155111.
  137. Ohmi, T., and K. Machida, 1998, J. Phys. Soc. Jpn. 67, 1822.
  138. Olshanii, M., and V. Yurovsky, 2009, arXiv:0911.5587.
  139. Pal, A., and D. A. Huse, 2010, Phys. Rev. B 82, 174411.
  140. Paraan, F. N. C., and A. Silva, 2009, Phys. Rev. E 80, 061130.
  141. Patanè, D., L. Amico, A. Silva, R. Fazio, and G. E. Santoro, 2009, Phys. Rev. B 80, 024302.
  142. Patanè, D., A. Silva, L. Amico, R. Fazio, and G. E. Santoro, 2008, Phys. Rev. Lett. 101, 175701.
  143. Patanè, D., A. Silva, F. Sols, and L. Amico, 2009, Phys. Rev. Lett. 102, 245701.
  144. Pauli, W., and M. Fierz, 1937, Z. Phys. 106, 572.
  145. Peres, A., 1984, Phys. Rev. A 30, 504.
  146. Plimak, L. I., M. Fleischhauer, M. K. Olsen, and M. J. Collett, 2001, arXiv:cond-mat/0102483.
  147. Poilblanc, D., T. Ziman, J. Bellissard, F. Mila, and G. Montambaux, 1993, Europhys. Lett. 22, 537.
  148. Polkovnikov, A., 2005, Phys. Rev. B 72, 161201(R).
  149. Polkovnikov, A., 2010a, Ann. Phys. (N.Y.) 326, 486.
  150. Polkovnikov, A., 2008b, Phys. Rev. Lett. 101, 220402.
  151. Polkovnikov, A., 2010b, Ann. Phys. (N.Y.) 325, 1790.
  152. Polkovnikov, A., and V. Gritsev, 2008, Nature Phys. 4, 477.
  153. Pollmann, F., S. Mukerjee, A. G. Green, and J. E. Moore, 2010, Phys. Rev. E 81, 020101.
  154. Popescu, S., A. J. Short, and A. Winter, 2006, Nature Phys. 2, 754.
  155. Porter, M., N. Zabusky, B. Hu, and D. Campbell, 2009, Am. Sci. 97, 214.
  156. Refael, G., and J. E. Moore, 2004, Phys. Rev. Lett. 93, 260602.
  157. C. Regal, and D. S. Jin, 2006, arXiv:cond-mat/0601054.
  158. Regal, S., 2006, Ph.D. thesis (University of Colorado, Boulder).
  159. Reimann, P., 2008, Phys. Rev. Lett. 101, 190403.
  160. Rey, A. M., B. L. Hu, E. Calzetta, and C. W. Clark, 2005, Phys. Rev. A 72, 023604.
  161. Rezakhani, A. T., D. F. Abasto, D. A. Lidar, and P. Zanardi, 2010, Phys. Rev. A 82, 012321.
  162. Rezakhani, A. T., W.-J. Kuo, A. Hamma, D. A. Lidar, and P. Zanardi, 2009, Phys. Rev. Lett. 103, 080502.
  163. Riedel, M. F., P. Böhi, Y. Li, T. W. Hänsch, A. Sinatra, and P. Treutlein, 2010, Nature (London) 464, 1170.
  164. Rigol, M., 2009, Phys. Rev. Lett. 103, 100403.
  165. Rigol, M., V. Dunjko, and M. Olshanii, 2008, Nature (London) 452, 854.
  166. Rigol, M., V. Dunjko, V. Yurovsky, and M. Olshanii, 2007, Phys. Rev. Lett. 98, 050405.
  167. Rigol, M., and L. F. Santos, 2010, Phys. Rev. A 82, 011604(R).
  168. Rigolin, G., G. Ortiz, and V. H. Ponce, 2008, Phys. Rev. A 78, 052508.
  169. Rivers, R., 2001, J. Low Temp. Phys. 124, 41.
  170. Rossini, D., A. Silva, G. Mussardo, and G. Santoro, 2010, Phys. Rev. B 82, 144302.
  171. Rossini, D., A. Silva, G. Mussardo, and G. E. Santoro, 2009, Phys. Rev. Lett. 102, 127204.
  172. Roux, G., 2009, Phys. Rev. A 79, 021608.
  173. Roux, G., 2010, Phys. Rev. A 81, 053604.
  174. Sachdev, S., 1999, Quantum Phase Transitions (Cambridge University Press, Cambridge, UK).
  175. Sadler, L. E., J. M. Higbie, S. R. Leslie, M. Vengalattore, and D. M. Stamper-Kurn, 2006, Nature (London) 443, 312.
  176. Saito, H., Y. Kawaguchi, and M. Ueda, 2007, Phys. Rev. A 76, 043613.
  177. Santos, L. F., and M. Rigol, 2010a, Phys. Rev. E 81, 036206.
  178. Santos, L. F., and M. Rigol, 2010b, Phys. Rev. E 82, 031130.
  179. Schmittmann, B., and R. Zia, 1995, Phase Transitions and Critical Phenomena, edited by C. Domb and J. Lebowitz (Academic Press, London), Vol. 17.
  180. Schollwöck, U., 2005, Rev. Mod. Phys. 77, 259.
  181. Schollwöck, U., and S. White, 2006, in Effective Models for Low-Dimensional Strongly Correlated Systems, edited by G. G. Batrouni and D. Poilblanc (AIP, Melville, NY), p. 155.
  182. Schwandt, D., F. Alet, and S. Capponi, 2009, Phys. Rev. Lett. 103, 170501.
  183. Sen, D., K. Sengupta, and S. Mondal, 2008, Phys. Rev. Lett. 101, 016806.
  184. Sen, D., and S. Vishveshwara, 2010, Europhys. Lett. 91, 66 009.
  185. Sengupta, K., S. Powell, and S. Sachdev, 2004, Phys. Rev. A 69, 053616.
  186. Sengupta, K., and D. Sen, 2009, Phys. Rev. A 80, 032304.
  187. Sengupta, K., D. Sen, and S. Mondal, 2008, Phys. Rev. Lett. 100, 077204.
  188. Sensarma, R., D. Pekker, E. Altman, E. Demler, N. Strohmaier, D. Greif, R. Jördens, L. Tarruell, H. Moritz, and T. Esslinger, 2010, Phys. Rev. B 82, 224302.
  189. Silva, A., 2008, Phys. Rev. Lett. 101, 120603.
  190. Sondhi, S. L., S. M. Girvin, J. P. Carini, and D. Shahar, 1997, Rev. Mod. Phys. 69, 315.
  191. Sorensen, A., L. M. Duan, J. I. Cirac, and P. Zoller, 2001, Nature (London) 409, 63.
  192. Srednicki, M., 1994, Phys. Rev. E 50, 888.
  193. Srednicki, M., 1999, J. Phys. A 32, 1163.
  194. Strohmaier, N., D. Greif, R. Jördens, L. Tarruell, H. Moritz, and T. Esslinger, 2010, Phys. Rev. Lett. 104, 080401.
  195. Stückelberg, E. C. G., 1932, Helv. Phys. Acta 5, 369.
  196. Sutherland, B., 2004, Beautiful Models (World Scientific, Singapore).
  197. Suzuki, M., 1971, Physica (Amsterdam) 51, 277.
  198. Tabor, M., 1989, Chaos and Integrability in Nonlinear Dynamics: An Introduction (Wiley, New York).
  199. Talkner, P., E. Lutz, and P. Hänggi, 2007, Phys. Rev. E 75, 050102.
  200. Thirring, W., 2002, Quantum Mathematical Physics (Springer, New York).
  201. Trotzky, S., P. Cheinet, S. Fölling, M. Feld, U. Schnorrberger, A. M. Rey, A. Polkovnikov, E. A. Demler, M. D. Lukin, and I. Bloch, 2008, Science 319, 295.
  202. Trotzky, S., Y.-A. Chen, A. Flesch, I. P. McCulloch, U. Schollwöck, I. B. J. Eisert, and I. Bloch, 2011, arXiv:1101.2659.
  203. Tuchman, A. K., C. Orzel, A. Polkovnikov, and M. Kasevich, 2006, Phys. Rev. A 74, 051601.
  204. Vengalattore, M., J. M. Higbie, S. R. Leslie, J. Guzman, L. E. Sadler, and D. M. Stamper-Kurn, 2007, Phys. Rev. Lett. 98, 200801.
  205. Vengalattore, M., S. R. Leslie, J. Guzman, and D. M. Stamper-Kurn, 2008, Phys. Rev. Lett. 100, 170403.
  206. Venuti, L. C., and P. Zanardi, 2007, Phys. Rev. Lett. 99, 095701.
  207. Verstraete, F., V. Murg, and J. Cirac, 2008, Adv. Phys. 57, 143.
  208. Vidal, G., 2003, Phys. Rev. Lett. 91, 147902.
  209. Vidal, G., 2004, Phys. Rev. Lett. 93, 040502.
  210. Vidal, G., J. I. Latorre, E. Rico, and A. Kitaev, 2003, Phys. Rev. Lett. 90, 227902.
  211. Vitanov, N. V., 1999, Phys. Rev. A 59, 988.
  212. Vitanov, N. V., and B. M. Garraway, 1996, Phys. Rev. A 53, 4288.
  213. Vojta, M., 2003, Rep. Prog. Phys. 66, 2069.
  214. von Neumann, J., 1929, Z. Phys. 57, 30.
  215. Walls, D., and G. Milburn, 1994, Quantum Optics (Springer-Verlag, Berlin).
  216. Weiler, C. N., T. W. Neely, D. R. Sherer, A. S. Bradley, M. J. Davis, and B. P. Anderson, 2008, Nature (London) 455, 948.
  217. White, S., 1992, Phys. Rev. Lett. 69, 2863.
  218. Widera, A., S. Trotzky, P. Cheinet, S. Fölling, F. Gerbier, and I. Bloch, 2008, Phys. Rev. Lett. 100, 140401.
  219. Yates, A., and W. H. Zurek, 1998, Phys. Rev. Lett. 80, 5477.
  220. Zabusky, N. J., and M. D. Kruskal, 1965, Phys. Rev. Lett. 15, 240.
  221. Zakharov, V., V. L’vov, and G. Falkovich, 1992, Kolmogorov Spectra of Turbulence (Springer-Verlag, Berlin), Vol. 1.
  222. Zener, C., 1932, Proc. R. Soc. A 137, 696.
  223. Zurek, W. H., 1985, Nature (London) 317, 505.
  224. Zurek, W. H., 1996, Phys. Rep. 276, 177.
  225. Zurek, W. H., 2003, Rev. Mod. Phys. 75, 715.
  226. Zurek, W. H., U. Dorner, and P. Zoller, 2005, Phys. Rev. Lett. 95, 105701.

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Rev. Mod. Phys. 83, 863– Published 15 August, 2011
  • Received 29 July 2010

© 2011 American Physical Society

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