\cal PT symmetry breaking and exceptional points for a class of inhomogeneous complex potentials

2009/07/21 by Patrick Dorey, Clare Dunning, Anna Lishman +1 · 1 citation
Mathematics · Physics and Astronomy · #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics #hep-th #math-ph #math.MP #quant-ph

paper · pdf · doi:10.1088/1751-8113/42/46/465302

published as J.Phys.A42:465302,2009 · 42 pages, many figures

arxiv created 2009/07/21 · openalex publication_date 2009/10/22 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

We study a three-parameter family of -symmetric Hamiltonians, related via the ODE/IM correspondence to the Perk–Schultz models. We show that real eigenvalues merge and become complex at quadratic and cubic exceptional points, and explore the corresponding Jordan block structures by exploiting the quasi-exact solvability of a subset of the models. The mapping of the phase diagram is completed using a combination of numerical, analytical and perturbative approaches. Among other things this reveals some novel properties of the Bender–Dunne polynomials, and gives new insight into a phase transition to infinitely many complex eigenvalues that was first observed by Bender and Boettcher. A new exactly solvable limit, the inhomogeneous complex square well, is also identified.

Citations

• Exceptional Points of Non-hermitian Operators
• Complex WKB analysis of a -symmetric eigenvalue problem

Cited by

• The Bethe ansatz and the Tzitzéica–Bullough–Dodd equation
• Parity-Time Symmetry in Hartree–Fock Theory

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