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Detecting broken PT-symmetry

Weigert, Stefan (orcid.org/0000-0002-6647-3252) (2006) Detecting broken PT-symmetry. Journal of Physics A: Mathematical and General. pp. 10239-10246. ISSN 0305-4470

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A fundamental problem in the theory of PT-invariant quantum systems is to determine whether a given system 'respects' this symmetry or not. If not, the system usually develops non-real eigenvalues. It is shown in this contribution how to algorithmically detect the existence of complex eigenvalues for a given PT-symmetric matrix. The procedure uses classical results from stability theory which qualitatively locate the zeros of real polynomials in the complex plane. The interest and value of the present approach lies in the fact that it avoids diagonalization of the Hamiltonian at hand.

Item Type: Article
Copyright, Publisher and Additional Information: © 2006 IOP Publishing Ltd. This is an author produced version of a paper published in Journal of Physics A: Mathematical and General.
Institution: The University of York
Academic Units: The University of York > Mathematics (York)
Depositing User: Repository Officer
Date Deposited: 13 Jun 2007
Last Modified: 07 Apr 2016 06:22
Published Version: http://dx.doi.org/10.1088/0305-4470/39/32/S22
Status: Published
Refereed: Yes
URI: http://eprints.whiterose.ac.uk/id/eprint/2523

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