Real Spectra in Non-Hermitian Hamiltonians HavingPTSymmetry

1997/12/31 by Carl M. Bender, Stefan Boettcher · 145 citations
Mathematics · Physics and Astronomy · #Bounded function #Eigenvalues and eigenvectors #Hamiltonian (control theory) #Hermitian matrix #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Photonic Systems #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #Spectral line #cond-mat #hep-th #math-ph #math.MP #quant-ph

paper · pdf · doi:10.1103/physrevlett.80.5243

published as Phys.Rev.Lett. 80 (1998) 5243-5246 · 5 pages, RevTex, 3 figures as epsf, as to appear in PRL

arxiv created 1998/05/06 · openalex publication_date 1998/06/15 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06

Abstract

The condition of self-adjointness ensures that the eigenvalues of a Hamiltonian are real and bounded below. Replacing this condition by the weaker condition of PT symmetry, one obtains new infinite classes of complex Hamiltonians whose spectra are also real and positive. These PT symmetric theories may be viewed as analytic continuations of conventional theories from real to complex phase space. This paper describes the unusual classical and quantum properties of these theories.

Citations

• Vortex pinning and non-Hermitian quantum mechanics

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