Detecting broken PT-symmetry

Stefan Weigert

doi:10.1088/0305-4470/39/32/S22

Detecting broken PT-symmetry

Stefan Weigert

Mathematics

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

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.

Original language	English
Pages (from-to)	10239-10246
Number of pages	8
Journal	Journal of Physics A: Mathematical and General
Volume	39
Issue number	32
DOIs	https://doi.org/10.1088/0305-4470/39/32/S22
Publication status	Published - 11 Aug 2006

Bibliographical note

Keywords

QUANTUM-MECHANICS
SQUARE-WELL
DIAGONALIZABILITY
SYSTEMS

Access to Document

10.1088/0305-4470/39/32/S22

weigerts30.pdf

Cite this

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title = "Detecting broken PT-symmetry",

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.",

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N2 - 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.

AB - 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.

KW - QUANTUM-MECHANICS

KW - SQUARE-WELL

KW - DIAGONALIZABILITY

KW - SYSTEMS

U2 - 10.1088/0305-4470/39/32/S22

DO - 10.1088/0305-4470/39/32/S22

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JF - Journal of Physics A: Mathematical and General

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