Quantum quench influenced by an excited-state phase transition

Pérez Fernández, P.; Cejnar, P.; Arias, J. M.; Dukelsky, J.; García Ramos, J. E.; Relaño Pérez, Armando

Quantum quench influenced by an excited-state phase transition

Download

Relano14libre.pdf (816.28 KB)

Official URL

http://dx.doi.org/10.1103/PhysRevA.83.033802

Publication date

2011

Authors

Relaño Pérez, Armando

Publisher

American Physical Society

Citations

Exportar

URI

https://hdl.handle.net/20.500.14352/44413

Citation

[1] J. Hertz, Phys. Rev. B 14, 1165 (1976). [2] R. Gilmore and D. H. Feng, Nucl. Phys. A 301, 189 (1978); R. Gilmore, J. Math. Phys. 20, 891 (1979). [3] R. Gilmore, Catastrophe Theory for Scientists and Engineers (Wiley, New York, 1981). [4] S. L. Sondhi, S. M. Girvin, J. P. Carini, and D. Shahar, Rev. Mod. Phys. 69, 315 (1997). [5] S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, 1999). [6] M. Vojta, Rep. Prog. Phys. 66, 2069 (2003). [7] R. F. Casten, Prog. Part. Nucl. Phys. 62, 183 (2009); P. Cejnar and J. Jolie, ibid. 62, 210 (2009). [8] P. Cejnar, J. Jolie, and R. F. Casten, Rev. Mod. Phys. 82, 2155 (2010). [9] K. Baumann, C. Guerlin, F. Brennecke, and T. Esslinger, Nature (London) 464, 1301 (2010); D. Nagy, G. Kónya, G. Szirmai, and P. Domokos, Phys. Rev. Lett. 104, 130401 (2010). [10] E. Barouch and M. Dresden, Phys. Rev. Lett. 23, 114 (1969). [11] M. Greiner, O. Mandel, T. Esslinger, T. Hänsch, and I. Bloch, Nature (London) 415, 39 (2002); M. Greiner, O. Mandel, T. Hänsch, and I. Bloch, ibid. 419, 51 (2002). [12] F. N. C. Paraan and A. Silva, Phys. Rev. E 80, 061130 (2009). [13] K. Sengupta, S. Powell, and S. Sachdev, Phys.Rev.A69, 053616 (2004). [14] A. Silva, Phys. Rev. Lett. 101, 120603 (2008). [15] L. Campos Venuti and P. Zanardi, Phys. Rev. A 81, 032113 (2010). [16] P. Cejnar, M.Macek, and S. Heinze, J. Phys. A 39, L515 (2006). [17] M. A. Caprio, P. Cejnar, and F. Iachello, Ann. Phys. (NY) 323, 1106 (2008). [18] P. Cejnar and P. Stráanský, Phys. Rev. E 78, 031130 (2008). [19] F. Leyvraz and W. D. Heiss, Phys. Rev. Lett. 95, 050402 (2005). [20] M. Reis, M. O. Terra Cunha, A. C. Oliviera, and M. C. Nemes, Phys. Lett. A 344, 164 (2005). [21] S. Heinze, P. Cejnar, J. Jolie, and M. Macek, Phys. Rev. C 73, 014306 (2006); M. Macek, P. Cejnar, J. Jolie, and S. Heinze, ibid. 73, 014307 (2006). [22] P. Ribeiro, J. Vidal, and R. Mosseri, Phys. Rev. Lett. 99, 050402 (2007); P. Ribeiro and T. Paul, Phys. Rev. A 79, 032107 (2009). [23] A. Relaño, J. M. Arias, and J. Dukelsky, Phys. Rev. A 78, 060102(R) (2008); P. Pérez Fernández, A. Relaño, J. M. Arias, J. Dukelsky, and J. E. García Ramos, ibid. 80, 032111 (2009). [24] F. Pérez Bernal and F. Iachello, Phys. Rev. A 77, 032115 (2008); 81, 050101(R) (2010). [25] R. Kanamoto, L. D. Carr, andM. Ueda, Phys. Rev. A 79, 063616 (2009); 81, 023625 (2010). [26] M. C. Figueiredo, T. M. Cotta, and G. Q. Pellegrino, Phys. Rev. E 81, 012104 (2010). [27] M. Kastner, S. Schreiber, and O. Schnetz, Phys. Rev. Lett. 99, 050601 (2007); M. Kastner, Rev. Mod. Phys. 80, 167 (2008). [28] I. Tikhonenkov, E. Pazy, Y. B. Band, and A. Vardi, Phys. Rev. A 77, 063624 (2008). [29] R. H. Dicke, Phys. Rev. 93, 99 (1954). [30] E. T. Jaynes and F. W. Cummings, Proc. IEEE 51, 89 (1963). [31] M. Tavis and F. W. Cummings, Phys. Rev. 170, 379 (1968). [32] K. Hepp and E. H. Lieb, Ann. Phys. (NY) 76, 360 (1973). [33] C. Emary and T. Brandes, Phys. Rev. E 67, 066203 (2003). [34] Dynamical Groups and Spectrum Generating Algebras, edited by A. Barut, A. Bohm, and Y. Ne’eman (World Scientific, Singapore, 1988). [35] A. Perelomov, Generalised Coherent States and their Applications (Springer, Berlin, 1986). [36] W.-M. Zhang, D. H. Feng, and R. Gilmore, Rev. Mod. Phys. 62, 867 (1990). [37] J. Kurchan, P. Leboeuf, and M. Saraceno, Phys. Rev. A 40, 6800 (1989). [38] O. Castaños, R. López Peña, E. Nahmad-Achar, J. G. Hirsch, E. López Moreno, and J. E. Vitela, Phys. Scr. 79, 065405 (2009). [39] M. C. Gutzwiller, J. Math. Phys. 12, 343 (1971); R. Balian and C. Bloch, Ann. Phys. (NY) 69, 76 (1972); M. V. Berry and M. Tabor, Proc. R. Soc. London, Ser. A 349, 101 (1976). [40] J. R. Cary and P. Rusu, Phys. Rev. A 47, 2496 (1993). [41] W. D. Heiss and M. Müller, Phys. Rev. E 66, 016217 (2002). [42] O. Babelon, L. Cantini, and B. Douc¸ot, J. Stat. Mech. P07011 (2009). [43] T. Gorin, T. Prosen, T. H. Seligman, and M. Žnidarič, Phys. Rep. 435, 33 (2006). [44] W. H. Zurek, Rev. Mod. Phys. 75, 715 (2003).

Abstract

We analyze excited-state quantum phase transitions (ESQPTs) in three schematic (integrable and nonintegrable) models describing a single-mode bosonic field coupled to a collection of atoms. It is shown that the presence of the ESQPT in these models affects the quantum relaxation processes following an abrupt quench in the control parameter. Clear-cut evidence of the ESQPT effects is presented in integrable models, while in a nonintegrable model the evidence is blurred due to chaotic behavior of the system in the region around the critical energy.

Description

©2011 American Physical Society. P.C. acknowledges useful discussions with M. Kastner and J. Hirsch. This work has been partially supported by the Czech Science Foundation (Grant No. 202/09/0084), by the Czech Ministry of Education (Grant No. MSM 0021620859), by the Spanish Ministerio de Educación y Ciencia and the European regional development fund FEDER (Grants No. FIS2009-07277, No. FIS2008-04189, No. FIS2006-12783-C03-01, No. FPA2006 13807-C02-02, No. FPA2007-63074, and No. FIS2009-11621-C02-01), by CPAN Ingenio (Grant No. CSPD-2007-00042 Ingenio), by Junta de Andalucía (Grants No. FQM160, No. FQM318, No. P05-FQM437, and No. P07-FQM-02962), and by the Universidad Complutense de Madrid (Grant No. UCM-910059). P.P-F. is supported by a FPU grant of the Spanish Ministerio de Educación y Ciencia. A.R. is supported by the Spanish program CPAN Consolider-ingenio.