Semiclassical approach to survival probability at quantum phase transitions

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 81, Issue 1, 2010, Pages

  Wang, Wen Ge ^a   Qin, Pinquan ^a   He, Lewei ^a   Wang, Ping ^a  

^a UNIVERSITY OF SCIENCE AND TECHNOLOGY OF CHINA   (China)

Author keywords

[No Author keywords available]

Indexed keywords

CLASSICAL COUNTERPART; CRITICAL POINTS; DEGREES OF FREEDOM; EXPONENTIAL DECAYS; GROUND LEVEL; POWER LAW DECAY; QUANTUM PHASE TRANSITIONS; SEMICLASSICAL APPROACHES; SEMICLASSICAL THEORIES; SURVIVAL PROBABILITIES;

EQUATIONS OF STATE; PROBABILITY;

PHASE TRANSITIONS;

EID: 76349112489     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.81.016214     Document Type: Article

References (46)

1. S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, 1999).
2. L. E. Sadler, Nature (London) 443, 312 (2006). 10.1038/nature05094 (Pubitemid 44435146)
3. M. Lewenstein, Adv. Phys. 56, 243 (2007). 10.1080/00018730701223200 (Pubitemid 46710973)
4. T. W. B. Kibble, J. Phys. A 9, 1387 (1976) 10.1088/0305-4470/9/8/029
5. T. W. B. Kibble, Phys. Rep. 67, 183 (1980). 10.1016/0370-1573(80)90091-5
6. W. H. Zurek, Nature (London) 317, 505 (1985) 10.1038/317505a0
7. W. H. Zurek, Phys. Rep. 276, 177 (1996). 10.1016/S0370-1573(96)00009-9 (Pubitemid 126164697)
8. J. Dziarmaga, A. Smerzi, W. H. Zurek, and A. R. Bishop, Phys. Rev. Lett. 88, 167001 (2002) 10.1103/PhysRevLett.88.167001
9. U. Dorner, P. Fedichev, D. Jaksch, M. Lewenstein, and P. Zoller, Phys. Rev. Lett. 91, 073601 (2003) 10.1103/PhysRevLett.91.073601
10. W. H. Zurek, U. Dorner, and P. Zoller, Phys. Rev. Lett. 95, 105701 (2005) 10.1103/PhysRevLett.95.105701
11. B. Damski and W. H. Zurek, Phys. Rev. Lett. 99, 130402 (2007). 10.1103/PhysRevLett.99.130402 (Pubitemid 47481401)
12. P. Felker and A. Zewail, Adv. Chem. Phys. 70, 265 (1988). 10.1002/9780470141199.ch8
13. H. T. Quan, Z. Song, X. F. Liu, P. Zanardi, and C. P. Sun, Phys. Rev. Lett. 96, 140604 (2006). 10.1103/PhysRevLett.96.140604
14. Z. G. Yuan, P. Zhang, and S. S. Li, Phys. Rev. A 75, 012102 (2007) 10.1103/PhysRevA.75.012102
15. Y. C. Li and S. S. Li, Phys. Rev. A 76, 032117 (2007). 10.1103/PhysRevA.76.032117 (Pubitemid 47510816)
16. D. Rossini, T. Calarco, V. Giovannetti, S. Montangero, and R. Fazio, Phys. Rev. A 75, 032333 (2007). 10.1103/PhysRevA.75.032333 (Pubitemid 46494670)
17. J. Zhang, X. Peng, N. Rajendran, and D. Suter, Phys. Rev. Lett. 100, 100501 (2008) 10.1103/PhysRevLett.100.100501
18. J. Zhang, F. M. Cucchietti, C. M. Chandrashekar, M. Laforest, C. A. Ryan, M. Ditty, A. Hubbard, J. K. Gamble, and R. Laflamme, Phys. Rev. A 79, 012305 (2009). 10.1103/PhysRevA.79.012305
19. In systems with finite N, the SP may show a periodic behavior for sufficiently long times. Here, we study the decay law of the SP for relatively long times in the thermodynamic limit.
20. At transition between localized and delocalized regimes, the SP may have power-law decay as shown in S. A. Schofield, P. G. Wolynes, and R. E. Wyatt, Phys. Rev. Lett. 74, 3720 (1995) 10.1103/PhysRevLett.74.3720
21. A. Ossipov, M. Weiss, T. Kottos, and T. Geisel, Phys. Rev. B 64, 224210 (2001). 10.1103/PhysRevB.64.224210
22. P. Zanardi and N. Paunković, Phys. Rev. E 74, 031123 (2006) 10.1103/PhysRevE.74.031123
23. L. C. Campos Venuti and P. Zanardi, Phys. Rev. Lett. 99, 095701 (2007) 10.1103/PhysRevLett.99.095701
24. W.-L. You, Y.-W. Li, and S.-J. Gu, Phys. Rev. E 76, 022101 (2007) 10.1103/PhysRevE.76.022101
25. S.-J. Gu, H. M. Kwok, W. Q. Ning, and H. Q. Lin, Phys. Rev. B 77, 245109 (2008). 10.1103/PhysRevB.77.245109
26. A. Peres, Phys. Rev. A 30, 1610 (1984). 10.1103/PhysRevA.30.1610
27. R. A. Jalabert and H. M. Pastawski, Phys. Rev. Lett. 86, 2490 (2001) 10.1103/PhysRevLett.86.2490
28. G. Benenti and G. Casati, Phys. Rev. E 65, 066205 (2002) 10.1103/PhysRevE.65.066205
29. T. Gorin, Phys. Rep. 435, 33 (2006) 10.1016/j.physrep.2006.09.003
30. Ph. Jacquod and C. Petitjean, Adv. Phys. 58, 67 (2009). 10.1080/00018730902831009
31. N. R. Cerruti and S. Tomsovic, Phys. Rev. Lett. 88, 054103 (2002) 10.1103/PhysRevLett.88.054103
32. N. R. Cerruti and S. Tomsovic, J. Phys. A 36, 3451 (2003). 10.1088/0305-4470/36/12/334
33. J. Vaníček and E. J. Heller, Phys. Rev. E 68, 056208 (2003). 10.1103/PhysRevE.68.056208
34. W.-G. Wang, G. Casati, and B. Li, Phys. Rev. E 69, 025201 (R) (2004) 10.1103/PhysRevE.69.025201
35. W.-G. Wang, G. Casati, B. Li, and T. Prosen, Phys. Rev. E 71, 037202 (2005). 10.1103/PhysRevE.71.037202
36. W.-G. Wang and B. Li, Phys. Rev. E 71, 066203 (2005). 10.1103/PhysRevE.71.066203
37. T. Prosen and M. Žnidarič, J. Phys. A 35, 1455 (2002). 10.1088/0305-4470/35/6/309 (Pubitemid 37026731)
38. Ph. Jacquod, I. Adagideli, and C. W. J. Beenakker, Europhys. Lett. 61, 729 (2003). 10.1209/epl/i2003-00289-y (Pubitemid 36357298)
39. W.-G. Wang, G. Casati, and B. Li, Phys. Rev. E 75, 016201 (2007). 10.1103/PhysRevE.75.016201 (Pubitemid 46134196)
40. The Gaussian shape of the initial state is irrelevant in the derivation of the power-law decay of ML (t). Moreover, as shown in, ML (t) has a long-time t-d decay for initial random states. These imply that the power-law feature might be insensitive to the initial condition.
41. Dividing M̄ L (t) in regular systems into diagonal and off-diagonal parts, Ref. shows that the off-diagonal part may have an exponential decay under certain condition.
42. R. H. Dicke, Phys. Rev. 93, 99 (1954). 10.1103/PhysRev.93.99
43. C. Emary and T. Brandes, Phys. Rev. E 67, 066203 (2003). 10.1103/PhysRevE.67.066203
44. H. J. Lipkin, N. Meshkov, and A. J. Glick, Nucl. Phys. 62, 188 (1965). 10.1016/0029-5582(65)90862-X
45. S. Dusuel and J. Vidal, Phys. Rev. B 71, 224420 (2005). 10.1103/PhysRevB.71.224420 (Pubitemid 41717918)
46. P. Wang, Q. Zheng, and W.-G. Wang (unpublished).