School Seminars and Colloquia

Complex WKB Analysis of a PT Symmetric Eigenvalue Problem

Mathematical Physics Seminar

by Mark Sorrell

Institution: Mathematics and Statistics, The University of Melbourne
Date: Mon 14th September 2009
Time: 1:00 PM
Location: Old Geolofy 2, The University of Melbourne

Abstract: There has recently been much interest in Hamiltonians that are non-Hermitian, but instead possess PT Symmetry, and may be found to still have an entirely real spectrum. The spectra of a particular class of PT symmetric eigenvalue problems has previously been studied by Dorey et al., and found to have an extremely rich structure. In this talk I present an explanation for these spec- tral properties in terms of quantisation conditions obtained from the complex WKB (Wentzel-Kramers-Brillouin) method. In particular, we consider the re- lation of the quantisation conditions to the reality and positivity properties of the eigenvalues as well as give an explanation of the previously observed pattern of eigenvalue degeneracies.

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