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

S. Weigert

doi:10.1088/1464-4266/5/3/380

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

S. Weigert

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	S416-S419
Number of pages	4
Journal	Journal of Optics B: Quantum and Semiclassical Optics
Volume	5
Issue number	3
DOIs	https://doi.org/10.1088/1464-4266/5/3/380
Publication status	Published - Jun 2003

Bibliographical note

Keywords

PT-symmetry
anti-linearity
anti-unitarity
invariances
representation theory

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10.1088/1464-4266/5/3/380

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Cite this

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title = "PT-symmetry and its spontaneous breakdown explained by anti-linearity",

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.",

keywords = "PT-symmetry, anti-linearity, anti-unitarity, invariances, representation theory",

author = "S. Weigert",

note = "{\textcopyright} 2003 IOP Publishing Ltd. This is an author produced version of a paper published in Journal of Optics B: Quantum and Semiclassical Optics.",

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AB - 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.

KW - PT-symmetry

KW - anti-linearity

KW - anti-unitarity

KW - invariances

KW - representation theory

U2 - 10.1088/1464-4266/5/3/380

DO - 10.1088/1464-4266/5/3/380

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JO - Journal of Optics B: Quantum and Semiclassical Optics

JF - Journal of Optics B: Quantum and Semiclassical Optics

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