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Detecting broken PT-symmetry

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Publication details

JournalJournal of Physics A: Mathematical and General
DatePublished - 11 Aug 2006
Issue number32
Volume39
Number of pages8
Pages (from-to)10239-10246
Original languageEnglish

Abstract

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.

Bibliographical note

© 2006 IOP Publishing Ltd. This is an author produced version of a paper published in Journal of Physics A: Mathematical and General.

    Research areas

  • QUANTUM-MECHANICS, SQUARE-WELL, DIAGONALIZABILITY, SYSTEMS

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