Universal dynamics near quantum critical points

Understanding Quantum Phase Transitions

Volumn , Issue , 2010, Pages 59-90

  Polkovnikov, Anatoli ^a   Gritsev, Vladimir ^b  

^a Boston University   (United States)

^b UNIVERSITY OF FRIBOURG   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85034626658     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1201/b10273     Document Type: Chapter

References (46)

1. S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, 1999).
2. S. L. Sondhi, S. M. Girvin, J. P. Carini, and D. Shahar, Rev. Mod. Phys. 69, 315 (1997).
3. M. Vojta, Rep. Prog. Phys. 66, 2069 (2003).
4. M. Greiner, O. Mandel, T. Esslinger, T. W. Hansch, and I. Bloch, Nature 415, 39 (2002).
5. M. P. A. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher, Phys. Rev. B 40, 546 (1989).
6. P. Calabrese and J. Cardy, Phys. Rev. Lett. 96, 136801 (2006).
7. P. Calabrese and J. Cardy, J. Stat. Mech: Th. and Exp. P06008, (2007).
8. A. Polkovnikov, Phys. Rev. B 72, R161201 (2005).
9. W. H. Zurek, U. Dorner, and P. Zoller, Phys. Rev. Lett. 95, 105701 (2005).
10. P. Reimann, Phys. Rev. Lett. 101, 190403 (2008).
11. M. Rigol, V. Dunjko, and M. Olshanii, Nature 452, 854 (2008).
12. A. Polkovnikov and V. Gritsev, Nat. Phys. 4, 477 (2008).
13. C. De Grandi and A. Polkovnikov, quot;Adiabatic perturbation theory: from Landau-Zener problem to quenching through a quantum critical point” in Quantum Quenching, Annealing and Computation, Eds. A. Das, A. Chandra, and B. K. Chakrabarti, Lect. Notes in Phys., vol. 802 (Springer, Heidelberg 2010), arXiv:0910.2236.
14. T. W. B Kibble, J. Phys. A 9, 1387 (1976).
15. W. H. Zurek, Phys. Rep. 276, 177 (1996).
16. L. C. Venuti and P. Zanardi, Phys. Rev. Lett. 99, 095701 (2007).
17. S.-J. Gu and H.-Q. Lin, Europhys. Lett. 87, 10003 (2009).
18. D. Schwandt, F. Alet, and S. Capponi, Phys. Rev. Lett. 103, 170501 (2009).
19. C. De Grandi, V. Gritsev, and A. Polkovnikov Phys. Rev. B 81, 012303 (2010); 0910.0876.
20. A. Polkovnikov, arXiv:0806.2862.
21. A. Polkovnikov, Phys. Rev. Lett. 101, 220402 (2008).
22. G. Rigolin, G. Ortiz, and V. H. Ponce, Phys. Rev. A 78, 052508 (2008).
23. D. Sen, K. Sengupta, and S.Mondal, Phys. Rev. Lett. 101, 016806 (2008).
24. R. Barankov and A. Polkovnikov, Phys. Rev. Lett. 101, 076801 (2008).
25. A. Kitaev, Ann. Phys. 321, 2 (2006).
26. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, Rev. Mod. Phys. 81, 109 (2009).
27. J. Dziarmaga, Phys. Rev. Lett. 95, 245701 (2005).
28. G. Rigolin, G. Ortiz, and V. H. Ponce, Phys. Rev. A 78, 052508 (2008).
29. R. Shankar, Principles of Quantum Mechanics (Springer, New York, 1994).
30. M. Tomka, V. Gritsev, and A. Polkovnikov, Geometric effects in quantum nonequilibrium dynamics, in preparation.
31. M. Eckstein and M. Kollar, arXiv:0911.1282.
32. D. Rossini, A. Silva, G. Mussardo, and G. E. Santoro, Phys. Rev. Lett. 102, 127204 (2009).
33. S. Sotiriadis, P. Calabrese, and J. Cardy, Europhys. Lett. 87, 20002 (2009).
34. I. Bloch, J. Dalibard, and W. Zwerger, Reviews of Modern Physics 80, 885 (2008).
35. L. D. Landau and E. M. Lifshitz, Statistical Physics, Third Edition, Part 1: Volume 5 (Butterworth-Heinemann, ADDRESS, 1980).
36. S. Lukyanov, Mod. Phys. Lett. A12, 2543 (1997).
37. A. Linde, Lect. Notes Phys. 738, 1 (2008).
38. T.S. Bunch and P. C. W. Davies, Proc. R. Soc. Lond. Ser. A 360, 117 (1978).
39. L. Landau, Phys. Z. Sovjetunion 1, 88 (1932).
40. C. Zener, Proc. R. Soc. London, Ser. A 137, 696 (1932).
41. E. Majorana, Nuovo Cimento 9, 43 (1932).
42. E. C. G. Stückelberg, Helv. Phys. Acta 5, 369 (1932).
43. B. Craps and O. Evnin, JHEP 0804, 021 (2008).
44. H. Liu, G. Moore, and N. Seiberg, JHEP 0206, 045 (2002).
45. N. A. Nekrasov, Surveys High Energ. Phys. 17, 115 (2002).
46. A. J. Tolley and N. Turok, Phys. Rev. D 66, 106005 (2002).