Classical trajectories for complex Hamiltonians

被引:44
作者
Bender, Carl M. [1 ]
Chen, Jun-Hua
Darg, Daniel W.
Milton, Kimball A.
机构
[1] Washington Univ, Dept Phys, St Louis, MO 63130 USA
[2] Univ London Imperial Coll Sci Technol & Med, Blackett Lab, London SW7 2BZ, England
来源
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL | 2006年 / 39卷 / 16期
关键词
D O I
10.1088/0305-4470/39/16/009
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
It has been found that complex non-Hermitian quantum-mechanical Hamiltonians may have entirely real spectra and generate unitary time evolution if they possess an unbroken PT symmetry. A well-studied class of such Hamiltonians is H = p(2)+x(2)(ix)(is an element of) (is an element of >= 0). This paper examines the underlying classical theory. Specifically, it explores the possible trajectories of a classical particle that is governed by this class of Hamiltonians. These trajectories exhibit an extraordinarily rich and elaborate structure that depends sensitively on the value of the parameter is an element of and on the initial conditions. A system for classifying complex orbits is presented.
引用
收藏
页码:4219 / 4238
页数:20
相关论文
共 7 条
[1]   Complex extension of quantum mechanics [J].
Bender, CM ;
Brody, DC ;
Jones, HF .
PHYSICAL REVIEW LETTERS, 2002, 89 (27)
[2]   Real spectra in non-Hermitian Hamiltonians having PT symmetry [J].
Bender, CM ;
Boettcher, S .
PHYSICAL REVIEW LETTERS, 1998, 80 (24) :5243-5246
[3]   PT-symmetric quantum mechanics [J].
Bender, CM ;
Boettcher, S ;
Meisinger, PN .
JOURNAL OF MATHEMATICAL PHYSICS, 1999, 40 (05) :2201-2229
[4]   Spectral equivalences, Bethe ansatz equations, and reality properties in PT-symmetric quantum mechanics [J].
Dorey, P ;
Dunning, C ;
Tateo, R .
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2001, 34 (28) :5679-5704
[5]  
Feigenbaum M. J., 1980, LOS ALAMOS SCI, V1, P4
[6]   Classical motion of complex 2-D non-Hermitian Hamiltonian systems [J].
Nanayakkara, A .
CZECHOSLOVAK JOURNAL OF PHYSICS, 2004, 54 (01) :101-107
[7]   Classical trajectories of 1D complex non-Hermitian Hamiltonian systems [J].
Nanayakkara, A .
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2004, 37 (15) :4321-4334