A remark on the Dunne-Unsal relation in exact semi-classics

Gahramanov, Ilmar; Tezgin, Kemal

doi:10.1103/PhysRevD.93.065037

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A remark on the Dunne-Unsal relation in exact semi-classics

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Gahramanov, Ilmar
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Gahramanov, I., & Tezgin, K. (2016). A remark on the Dunne-Unsal relation in exact semi-classics. Physical Review D, 93: 065037. doi:10.1103/PhysRevD.93.065037.

Zitierlink: https://hdl.handle.net/11858/00-001M-0000-002A-12DC-2

Zusammenfassung

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.