A resurgence analysis for cubic and quartic anharmonic potentials

Abstract

In this work we explicitly show resurgence relations between perturbative and one instanton sectors of the resonance energy levels for cubic and quartic anharmonic potentials in one-dimensional quantum mechanics. Both systems satisfy the Dunne-Unsal relation and hence we are able to derive one-instanton non-perturbative contributions with the fluctuation terms to the energy merely from the perturbative data. We confirm our results with previous results obtained by Zinn-Justin et al.

9 pages

References in corpus (4)

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• Imaginary Cubic Perturbation: Numerical and Analytic Study
• Remark on the Dunne-Unsal relation in exact semi-classics
• Unified Treatment of Even and Odd Anharmonic Oscillators of Arbitrary Degree

Cited by in corpus (5)

• A Primer on Resurgent Transseries and Their Asymptotics
• Unified genus-1 potential and a parametric perturbative/nonperturbative relation
• Resurgence of deformed genus-1 curves: A novel perturbative/nonperturbative relation
• Numerical and Fitting Approach for Investigation of the Schrödinger Equation for Flat Potentials
• WKB and "Cubic-WKB" methods as an adiabatic approximation