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PT-symmetry and its spontaneous breakdown explained by anti-linearity

Weigert, S. (2003) PT-symmetry and its spontaneous breakdown explained by anti-linearity. Journal of Optics B: Quantum and Semiclassical Optics. S416-S419. ISSN 1464-4266

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Abstract

The impact of an anti-unitary symmetry on the spectrum of non-Hermitian operators is studied. Wigner's normal form of an anti-unitary operator accounts for the spectral properties of non-Hermitian, PE-symmetric Harniltonians. The occurrence of either single real or complex conjugate pairs of eigenvalues follows from this theory. The corresponding energy eigenstates span either one- or two-dimensional irreducible representations of the symmetry PE. In this framework, the concept of a spontaneously broken PE-symmetry is not needed.

Item Type: Article
Copyright, Publisher and Additional Information: © 2003 IOP Publishing Ltd. This is an author produced version of a paper published in Journal of Optics B: Quantum and Semiclassical Optics.
Keywords: PT-symmetry, anti-linearity, anti-unitarity, invariances, representation theory
Institution: The University of York
Academic Units: The University of York > Mathematics (York)
Depositing User: Repository Officer
Date Deposited: 22 Jun 2006
Last Modified: 16 Oct 2014 17:44
Published Version: http://dx.doi.org/10.1088/1464-4266/5/3/380
Status: Published
Refereed: Yes
Related URLs:
URI: http://eprints.whiterose.ac.uk/id/eprint/1356

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