×
Mandal, Bhabani Prasad; Mourya, Brijesh Kumar; Yadav, Rajesh Kumar

PT phase transition in higher-dimensional quantum systems. (English) Zbl 1279.81046

Phys. Lett., A 377, No. 14, 1043-1046 (2013).
Summary: We consider a 2d anisotropic SHO with \(ixy\) interaction and a 3d SHO in an imaginary magnetic field with \(\vec\mu_l.\vec B\) interaction to study the \(PT\) phase transition analytically in higher dimension. Unbroken \(PT\) symmetry in the first case is complementary to the rotational symmetry of the original Hermitian system. \(PT\) phase transition ceases to occur the moment the 2d oscillator becomes isotropic. Transverse magnetic field in the other system introduces the anisotropy in the system and the system undergoes \(PT\) phase transition depending on the strength of the magnetic field and frequency of the oscillator. All these results in higher dimensions are based on exact analytical calculations.

Cited in 11 Documents

MSC:

81Q12 Nonselfadjoint operator theory in quantum theory including creation and destruction operators
81R40 Symmetry breaking in quantum theory

Keywords:

non-Hermitian quantum mechanics; \(PT\) symmetry breaking in higher dimensions; anisotropy and \(PT\) phase transition
Cite Review PDF
Full Text: DOI arXiv

References:

[1] Bender, C. M.; Boettcher, S., Phys. Rev. Lett., 80, 5243 (1998) · Zbl 0947.81018
[2] Bender, C. M., Rep. Prog. Phys., 70, 947 (2007), and references therein
[3] Mostafazadeh, A., Int. J. Geom. Math. Mod. Phys., 7, 1191 (2010), and references therein · Zbl 1208.81095
[4] Bender, C. M.; Boettcher, S., Phys. Rev. Lett., 89, 270401 (1998)
[5] Khare, A.; Mandal, B. P., Phys. Lett. A, 272, 53 (2000) · Zbl 1115.81395
[6] Bender, C. M.; Jones, H. F., Phys. Lett. A, 328, 102 (2004) · Zbl 1134.81373
[7] Mostafazadeh, A.; Zamani, F., Ann. Phys., 321, 2210 (2006) · Zbl 1104.81042
[8] Mostafazadeh, A., J. Phys. A: Math. Theor., 44, 375302 (2009)
[9] Ahmed, Z., Phys. Lett. A, 287, 295 (2001)
[10] Ahmed, Z., J. Phys. A: Math. Theor., 42, 473005 (2001)
[11] Khare, A.; Mandal, B. P., Pramana J. Phys., 73, Special issue, 387 (2009)
[12] Basu-Mallick, B.; Bhattacharyya, T.; Kundu, A.; Mandal, B. P., Czech. J. Phys., 54, 5 (2004)
[13] Basu-Mallick, B.; Bhattacharyya, T.; Mandal, B. P., Mod. Phys. Lett. A, 20, 543 (2004)
[14] Mandal, B. P.; Ghatak, A., J. Phys. A: Math. Gen., 45, 444022 (2012) · Zbl 1263.81192
[15] Mandal, B. P.; Gupta, S., Mod. Phys. Lett. A, 25, 1723 (2010) · Zbl 1193.81030
[16] Mandal, B. P., Mod. Phys. Lett. A, 20, 655 (2005) · Zbl 1067.81535
[17] Ghatak, A.; Mandal, B. P., J. Phys. A: Math. Gen., 45, 355301 (2012) · Zbl 1252.81012
[18] Bagchi, B.; Quesne, C., Phys. Lett. A, 273, 256 (2000) · Zbl 1050.81546
[19] Abhinav, K.; Panigrahi, P. K., Ann. Phys., 326, 538 (2011) · Zbl 1208.81105
[20] Ghatak, A.; Nathan, Z. A.; Mandal, B. P.; Ahmed, Z., J. Phys. A: Math. Gen., 45, 465305 (2012) · Zbl 1258.81035
[21] Musslimani, Z. H.; Makris, K. G.; El-Ganainy, R.; Christodulides, D. N., Phys. Rev. Lett., 100, 030402 (2008)
[22] Ruter, C. E.; Makris, K. G.; El-Ganainy, R.; Christodulides, D. N.; Segev, M.; Kip, D., Nature Phys. (London), 6, 192 (2010)
[23] Guo, A.; Salamo, G. J., Phys. Rev. Lett., 103, 093902 (2009)
[24] Bender, C. M.; Boettcher, S.; Meisinger, P. N., J. Math. Phys., 40, 2201 (1999) · Zbl 1057.81512
[25] West, C. T.; Kottos, T.; Prosen, T., Phys. Rev. Lett., 104, 054102 (2010)
[26] Bender, C. M.; Berntson, B. K.; Parker, D.; Samuel, E.
[27] Schindler, J.; Li, A.; Zheng, M. C.; Ellis, F. M.; Kottos, T., Phys. Rev. A, 84, 040101 (2011)
[28] Ramezani, H.; Schindler, J.; Ellis, F. M.; Kottos, T., Phys. Rev. A, 85, 062122 (2012)
[29] Lin, Z.; Schindler, J.; Ellis, F. M.; Kottos, T., Phys. Rev. A, 85, 050101(R) (2012)
[30] Bender, C. M.; Dunne, G. V.; Meisinger, P. N.; Simsek, M., Phys. Lett. A, 281, 311 (2001) · Zbl 0984.81042
[31] Bender, C. M.; Berryand, M.; Mandilara, A., J. Phys., 35, L467 (2002) · Zbl 1066.81537
[32] Znojil, M., J. Phys. A, 36, 7825 (2003)
[33] Levai, G., J. Phys. A, 41, 244015 (2008) · Zbl 1140.81414
[34] Bender, C. M.; Weir, D. J.
[35] Nanayakkara, A., Phys. Lett. A, 304, 67 (2002) · Zbl 0999.81022
[36] Hatano, N.; Nelson, D. R., Phys. Rev. B, 58, 8384 (1998)
[37] Hatano, N.; Nelson, D. R., Phys. Rev. Lett., 77, 570 (1996)
[38] Bazeia, D.; Das, A.; Losano, L., Phys. Lett. B, 673, 283 (2009)
[39] Wigner, E., J. Math. Phys., 1, 409 (1960) · Zbl 0096.43401
[40] Dey, S.; Fring, A.; Gouba, L., J. Phys. A, 45, 385302 (2012)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.