$1/\epsilon$ problem in resurgence

Abstract

This paper considers the $1/\epsilon$ problem, which is the divergent behavior of the ground state energy of asymmetric potential in quantum mechanics, which is calculated with semi-classical expansion and resurgence technique. Using resolvent method, It is shown that including not only one complex bion but multi-complex bion and multi-bounce contributions solves this problem. This result indicates the importance of summing all possible saddle points contribution and also the relationship between exact WKB and path integral formalism.

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• Exact WKB and the quantum Seiberg-Witten curve for 4d $N=2$ pure $SU(3)$ Yang-Mills, Part I: Abelianization
• Quantum phase transition and Resurgence: Lessons from 3d $\mathcal{N}=4$ SQED
• TBA equations and exact WKB analysis in deformed supersymmetric quantum mechanics
• Exact WKB in all sectors I: Potentials with degenerate saddles
• Exact-WKB Analysis of Two-level Floquet Systems
• Exact WKB in all sectors II: Potentials with non-degenerate saddles