Partition functions and zeta functions of homogeneous Hermitian and PT-symmetric oscillators are computed from contour integrals of the ODE/IM counting function a(E) obtained from the Destri-de Vega equation.
Beyond the WKB approximation in PT-symmetric quantum mechanics
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abstract
The mergings of energy levels associated with the breaking of PT symmetry in the model of Bender and Boettcher, and in its generalisation to incorporate a centrifugal term, are analysed in detail. Even though conventional WKB techniques fail, it is shown how the ODE/IM correspondence can be used to obtain a systematic approximation scheme which captures all previously-observed features. Nonperturbative effects turn out to play a crucial role, governing the behaviour of almost all levels once the symmetry-breaking transition has been passed. In addition, a novel treatment of the radial Schrodinger equation is used to recover the values of local and non-local conserved charges in the related integrable quantum field theories, without any need for resummation even when the angular momentum is nonzero.
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Partition Functions of Hermitian and PT-Symmetric Oscillators from Integrable Models
Partition functions and zeta functions of homogeneous Hermitian and PT-symmetric oscillators are computed from contour integrals of the ODE/IM counting function a(E) obtained from the Destri-de Vega equation.