Critical parameters for non-hermitian Hamiltonians

被引：5

作者：

Fernandez, Francisco M. ^{[1
]}

Garcia, Javier ^{[1
]}

机构：

[1] UNLP, CCT La Plata CONICET, INIFTA, Div Quim Teor, RA-1900 La Plata, Buenos Aires, Argentina

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2014年 / 247卷

关键词：

PT symmetry; Non-hermitian Hamiltonians; Critical parameters; Exceptional points; Diagonalization method; EXCEPTIONAL POINTS; SQUARE-WELL; SPONTANEOUS BREAKDOWN; SYMMETRY; OPERATOR;

D O I：

10.1016/j.amc.2014.08.083

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We calculate accurate critical parameters for a class of non-hermitian Hamiltonians by means of the diagonalization method. We study three one-dimensional models and two perturbed rigid rotors with PT symmetry. One of the latter models illustrates the necessity of a more general condition for the appearance of real eigenvalues that we also discuss here. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：141 / 151

页数：11

共 19 条

[1]

Abramowitz M., 1972, HDB MATH FUNCTIONS

[2] PT phase transition in multidimensional quantum systems [J].

Bender, Carl M. ;

Weir, David J. .

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2012, 45 (42)

[3]

Bender CM, 2011, INT J THEOR PHYS, V50, P955, DOI 10.1007/s10773-010-0511-2

[4] The C operator in PT-symmetric quantum theories [J].

Bender, CM ;

Brod, J ;

Refig, A ;

Reuter, ME .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2004, 37 (43) :10139-10165

[5] Calculation of the hidden symmetry operator in PT-symmetric quantum mechanics [J].

Bender, CM ;

Meisinger, PN ;

Wang, QH .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2003, 36 (07) :1973-1983

[6] Complex WKB analysis of energy-level degeneracies of non-Hermitian Hamiltonians [J].

Bender, CM ;

Berry, M ;

Meisinger, PN ;

Savage, VM ;

Simsek, M .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2001, 34 (06) :L31-L36

[7] Spectral analysis of the complex cubic oscillator [J].

Delabaere, E ;

Trinh, DT .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2000, 33 (48) :8771-8796

[8]

Fernandez FranciscoM, 2001, INTRO PERTURBATION T, VFirst

[9] Orthogonal polynomial projection quantization: a new Hill determinant method [J].

Handy, C. R. ;

Vrinceanu, D. .

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2013, 46 (13)

[10] Spectral bounds for the PT-breaking Hamiltonian p2+x4+iax [J].

Handy, CR ;

Wang, XQ .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2003, 36 (45) :11513-11532

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