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

By S. Weigert

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

Year: 2003
DOI identifier: 10.1088/1464-4266
OAI identifier: oai:eprints.whiterose.ac.uk:1356

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