Adiabatic dynamics of a quantum critical system coupled to an environment: Scaling and kinetic equation approaches

Physical Review B - Condensed Matter and Materials Physics

Volumn 80, Issue 2, 2009, Pages

  Patanè, Dario ^a   Amico, Luigi ^a   Silva, Alessandro ^b,c   Fazio, Rosario ^d   Santoro, Giuseppe E ^c,e,f  

^a UNIVERSITY OF CATANIA   (Italy)

^b UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

^c ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS   (Italy)

^d INFM   (Italy)

^e SISSA   (Italy)

^f DEMOCRITOS NATIONAL SIMULATION CENTER   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 68949092628     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.80.024302     Document Type: Article

References (73)

1. M. Greiner, Olaf Mandel, Tilman Esslinger, Theodor W. Hänsch, and Immanuel Bloch, Nature (London) 415, 39 (2002) 10.1038/415039a
2. M. Greiner, Olaf Mandel, Theodor W. Hänsch, and Immanuel Bloch, Nature (London) 419, 51 (2002). 10.1038/nature00968
3. T. Kinoshita, T. Wenger, and D. S. Weiss, Nature (London) 440, 900 (2006). 10.1038/nature04693
4. L. E. Sadler, J. M. Higbie, S. R. Leslie, M. Vengalattore, and D. M. Stamper-Kurn, Nature (London) 443, 312 (2006). 10.1038/nature05094
5. F. Iglói and H. Rieger, Phys. Rev. Lett. 85, 3233 (2000) 10.1103/PhysRevLett.85.3233
6. K. Sengupta, S. Powell, and S. Sachdev, Phys. Rev. A 69, 053616 (2004) 10.1103/PhysRevA.69.053616
7. P. Calabrese and J. Cardy, Phys. Rev. Lett. 96, 136801 (2006) 10.1103/PhysRevLett.96.136801
8. P. Calabrese and J. Cardy, J. Stat. Mech.: Theory Exp. (2007) P10004 10.1088/1742-5468/2007/10/P10004
9. G. De Chiara, S. Montangero, and P. Calabrese, R. Fazio, J. Stat. Mech.: Theory Exp. (2006) P03001 10.1088/1742-5468/2006/03/P03001
10. S. Montangero, R. Fazio, P. Zoller, and G. Pupillo, Phys. Rev. A 79, 041602 (R) (2009) 10.1103/PhysRevA.79.041602
11. D. Rossini, A. Silva, G. Mussardo, and G. Santoro, Phys. Rev. Lett. 102, 127204 (2009) 10.1103/PhysRevLett.102.127204
12. P. Barmettler, M. Punk, V. Gritsev, E. Demler, and E. Altman, Phys. Rev. Lett. 102, 130603 (2009). 10.1103/PhysRevLett.102.130603
13. M. Rigol, V. Dunjko, V. Yurovsky, and M. Olshanii, Phys. Rev. Lett. 98, 050405 (2007) 10.1103/PhysRevLett.98.050405
14. C. Kollath, A. M. Läuchli, and E. Altman, Phys. Rev. Lett. 98, 180601 (2007) 10.1103/PhysRevLett.98.180601
15. S. R. Manmana, S. Wessel, R. M. Noack, and A. Muramatsu, Phys. Rev. Lett. 98, 210405 (2007) 10.1103/PhysRevLett.98.210405
16. M. Cramer, C. M. Dawson, J. Eisert, and T. J. Osborne, Phys. Rev. Lett. 100, 030602 (2008) 10.1103/PhysRevLett.100.030602
17. T. Barthel and U. Schollwock, Phys. Rev. Lett. 100, 100601 (2008) 10.1103/PhysRevLett.100.100601
18. M. Eckstein and M. Kollar, Phys. Rev. Lett. 100, 120404 (2008) 10.1103/PhysRevLett.100.120404
19. M. A. Cazalilla, Phys. Rev. Lett. 97, 156403 (2006) 10.1103/PhysRevLett. 97.156403
20. D. M. Gangardt and M. Pustilnik, Phys. Rev. A 77, 041604 (R) (2008). 10.1103/PhysRevA.77.041604
21. A. Polkovnikov, Phys. Rev. Lett. 101, 220402 (2008) 10.1103/PhysRevLett. 101.220402
22. R. Barankov and A. Polkovnikov, arXiv:0806.2862 (unpublished).
23. A. Silva, Phys. Rev. Lett. 101, 120603 (2008) 10.1103/PhysRevLett.101. 120603
24. G. Roux, Phys. Rev. A 79, 021608 (R) (2009) 10.1103/PhysRevA.79.021608
25. A. Faribault, P. Calabrese, and J.-S. Caux, J. Stat. Mech.: Theory Exp. (2009) P03018. 10.1088/1742-5468/2009/03/P03018
26. T. W. B. Kibble, J. Phys. A 9, 1387 (1976) 10.1088/0305-4470/9/8/029
27. W. H. Zurek, Nature (London) 317, 505 (1985). 10.1038/317505a0
28. T. W. B. Kibble, Phys. Today 60 (9), 47 (2007). 10.1063/1.2784684
29. E. Farhi, Jeffrey Goldstone, Sam Gutmann, Joshua Lapan, Andrew Lundgren, and Daniel Preda, Science 292, 472 (2001). 10.1126/science.1057726
30. G. E. Santoro, Roman Martonak, Erio Tosatti, and Roberto Car, Science 295, 2427 (2002). 10.1126/science.1068774
31. G. E. Santoro and E. Tosatti, J. Phys. A 39, R393 (2006). 10.1088/0305-4470/39/36/R01
32. W. H. Zurek, U. Dorner, and P. Zoller, Phys. Rev. Lett. 95, 105701 (2005). 10.1103/PhysRevLett.95.105701
33. A. Polkovnikov, Phys. Rev. B 72, 161201 (R) (2005). 10.1103/PhysRevB.72. 161201
34. J. Dziarmaga, Phys. Rev. Lett. 95, 245701 (2005). 10.1103/PhysRevLett.95. 245701
35. B. Damski, Phys. Rev. Lett. 95, 035701 (2005). 10.1103/PhysRevLett.95. 035701
36. R. Schutzhold, M. Uhlmann, Y. Xu, and U. R. Fischer, Phys. Rev. Lett. 97, 200601 (2006). 10.1103/PhysRevLett.97.200601
37. R. W. Cherng and L. S. Levitov, Phys. Rev. A 73, 043614 (2006). 10.1103/PhysRevA.73.043614
38. B. Damski and W. H. Zurek, Phys. Rev. Lett. 99, 130402 (2007). 10.1103/PhysRevLett.99.130402
39. F. M. Cucchietti, B. Damski, J. Dziarmaga, and W. H. Zurek, Phys. Rev. A 75, 023603 (2007). 10.1103/PhysRevA.75.023603
40. L. Cincio, J. Dziarmaga, M. M. Rams, and W. H. Zurek, Phys. Rev. A 75, 052321 (2007). 10.1103/PhysRevA.75.052321
41. T. Caneva, R. Fazio, and G. E. Santoro, Phys. Rev. B 76, 144427 (2007). 10.1103/PhysRevB.76.144427
42. T. Caneva, R. Fazio, and G. E. Santoro, Phys. Rev. B 78, 104426 (2008). 10.1103/PhysRevB.78.104426
43. K. Sengupta, D. Sen, and S. Mondal, Phys. Rev. Lett. 100, 077204 (2008). 10.1103/PhysRevLett.100.077204
44. A. Polkovnikov and V. Gritsev, Nat. Phys. 4, 477 (2008). 10.1038/nphys963
45. D. Sen, K. Sengupta, and S. Mondal, Phys. Rev. Lett. 101, 016806 (2008). 10.1103/PhysRevLett.101.016806
46. U. Divakaran, V. Mukherjee, A. Dutta, and D. Sen, J. Stat. Mech.: Theory Exp. (2009) P02007. 10.1088/1742-5468/2009/02/P02007
47. F. Pellegrini, S. Montangero, G. E. Santoro, and R. Fazio, Phys. Rev. B 77, 140404 (R) (2008). 10.1103/PhysRevB.77.140404
48. S. Deng, G. Ortiz, and L. Viola, EPL 84, 67008 (2008). 10.1209/0295-5075/84/67008
49. A. Fubini, G. Falci, and A. Osterloh, New J. Phys. 9, 134 (2007). 10.1088/1367-2630/9/5/134
50. S. Mostame, G Schaller, and R. Schützhold, Phys. Rev. A 76, 030304 (R) (2007). 10.1103/PhysRevA.76.030304
51. M. H. S. Amin, C. J. S. Truncik, and D. V. Averin, arXiv:0803.1196 (unpublished).
52. L. Cincio, J. Dziarmaga, J. Meisner, and M. M. Rams, Phys. Rev. B 79, 094421 (2009). 10.1103/PhysRevB.79.094421
53. D. Patanè, A. Silva, L. Amico, R. Fazio, and G. E. Santoro, Phys. Rev. Lett. 101, 175701 (2008). 10.1103/PhysRevLett.101.175701
54. S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, 1999).
55. Notice that depending on the characteristics of the bath, the system-bath coupling may lead to a change in universality class of the transition as a result of bath-induced long-range correlations effects. We will not address these issues here, which deserve a careful separate study. Therefore we will assume the bath correlations to be short ranged in time (Ref.).
56. P. Pfeuty, Ann. Phys. 57, 79 (1970). 10.1016/0003-4916(70)90270-8
57. U. Weiss, Quantum Dissipative Systems (World Scientific, Singapore, 1992).
58. L. S. Levitov, T. P. Orlando, J. B. Majer, and J. E. Mooij, arXiv:cond-mat/0108266 (unpublished).
59. E. Paladino, L. Faoro, G. Falci, and R. Fazio, Phys. Rev. Lett. 88, 228304 (2002). 10.1103/PhysRevLett.88.228304
60. J. A. Hoyos and T. Vojta, Phys. Rev. Lett. 100, 240601 (2008) 10.1103/PhysRevLett.100.240601
61. T. Vojta and J. A. Hoyos, arXiv:0811.3754 (unpublished)
62. J. A. Hoyos, C. Kotabage, and T. Vojta, Phys. Rev. Lett. 99, 230601 (2007) 10.1103/PhysRevLett.99.230601
63. G. Schehr and H. Rieger, J. Stat. Mech.: Theory Exp. (2008) P04012 10.1088/1742-5468/2008/04/P04012
64. G. Schehr and H. Rieger, Phys. Rev. Lett. 96, 227201 (2006). 10.1103/PhysRevLett.96.227201
65. P. P. Orth, I. Stanic and K. Le Hur, Phys. Rev. A 77, 051601 (R) (2008). 10.1103/PhysRevA.77.051601
66. J. Rammer and H. Smith, Rev. Mod. Phys. 58, 323 (1986). 10.1103/RevModPhys.58.323
67. H. Haug and A.-P. Jauho, Quantum Kinetics in Transport and Optics of Semiconductors (Springer, Berlin, 1996).
68. R. van Leeuwen, N. E. Dahlen, G. Stefanucci, C.-O. Almbladh, and U. von Barth, arXiv:cond-mat/0506130 (unpublished).
69. P. Werner, K. Volker, M. Troyer, and S. Chakravarty, Phys. Rev. Lett. 94, 047201 (2005) 10.1103/PhysRevLett.94.047201
70. P. Werner, M. Troyer, and S. Sachdev, J. Phys. Soc. Jpn. Suppl. 74, 67 (2005).
71. L. Landau, Phys. Z. Sowjetunion 2, 46 (1932)
72. C. Zener, Proc. R. Soc. London, Ser. A 137, 696 (1932). 10.1098/rspa.1932.0165
73. C. Cohen-Tannoudji, J. Dupont-Roc, G. Grynberg, Atom-photon interactions: Basic processes and applications (Wiley-Hermann, New York, 1992).