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Remark on the Dunne-Unsal relation in exact semi-classics

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arxiv 1512.08466 v3 pith:3CZBFO4P submitted 2015-12-28 hep-th cond-mat.othermath-phmath.MPquant-ph

Ilmar Gahramanov , Kemal Tezgin This is my paper · ORCID
classification hep-thcond-mat.othermath-phmath.MPquant-ph
keywords relationanharmonicdunne-unsalgenushigheroscillatorspotentialsapplicable
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Recently, it is realized that non-perturbative instanton effects can be generated to all orders by perturbation theory around a degenerate minima via Dunne-Unsal relation in several quantum mechanical systems. In this work we verify the Dunne-Unsal relation for resonance energy levels of one-dimensional polynomial anharmonic oscillators. We show that the relation is applicable to cubic and quartic anharmonic oscillators which are genus one potentials. However for higher order (higher genus) anharmonic potentials the relation is not satisfied and is subject to a certain extension.

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  1. Exact WKB in all sectors II: Potentials with non-degenerate saddles

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    For generic one-dimensional potentials, the exact spectrum decomposes into as many trans-series sectors as there are distinct local-minimum energy levels, with continuous transitions across barrier tops and discontinu...

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