Spectral singularities in PT-symmetric periodic finite-gap systems

被引:48
|
作者
Correa, Francisco [1 ]
Plyushchay, Mikhail S. [2 ]
机构
[1] Ctr Estudios Cient, Valdivia, Chile
[2] Univ Santiago Chile, Dept Fis, Santiago 2, Chile
来源
PHYSICAL REVIEW D | 2012年 / 86卷 / 08期
关键词
NON-HERMITIAN HAMILTONIANS; EXCEPTIONAL POINTS; SUSY TRANSFORMATIONS; POTENTIALS; REAL; SUPERSYMMETRY;
D O I
10.1103/PhysRevD.86.085028
中图分类号
P1 [天文学];
学科分类号
0704 ;
摘要
The origin of spectral singularities in finite-gap singly periodic PT-symmetric quantum systems is investigated. We show that they emerge from a limit of band-edge states in a doubly periodic finite gap system when the imaginary period tends to infinity. In this limit, the energy gaps are contracted and disappear, every pair of band states of the same periodicity at the edges of a gap coalesces and transforms into a singlet state in the continuum. As a result, these spectral singularities turn out to be analogous to those in the nonperiodic systems, where they appear as zero-width resonances. Under the change of topology from a noncompact into a compact one, spectral singularities in the class of periodic systems we study are transformed into exceptional points. The specific degeneration related to the presence of finite number of spectral singularities and exceptional points is shown to be coherently reflected by a hidden, bosonized nonlinear supersymmetry.
引用
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页数:9
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