$1/\epsilon$ problem in resurgence

TL;DR

This paper addresses the divergence in ground state energy calculations for asymmetric potentials using resurgence, showing that summing multiple saddle points resolves the $1/$ problem and clarifies the link between WKB and path integrals.

Contribution

It demonstrates that including multi-bion and multi-bounce contributions in resurgence techniques resolves the $1/$ divergence in quantum mechanical energy calculations.

Findings

Including multi-bion contributions solves the divergence problem.

Resurgence links exact WKB and path integral formalism.

Summing all saddle points is crucial for accurate energy calculations.

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.