Trans-series for the ground state density and Generalized Bloch equation

TL;DR

This paper develops a trans-series expansion for the ground state density phase in a double-well potential using the Generalized Bloch equation, revealing non-perturbative corrections linked to instanton contributions.

Contribution

It introduces a novel trans-series approach for the ground state density phase, incorporating non-perturbative effects from multi-instanton trajectories within the Generalized Bloch framework.

Findings

Leading semiclassical terms are determined by flucton trajectories.

Next-to-leading terms involve quadratic fluctuations (determinant).

Next-to-next-to-leading corrections are non-perturbative and related to instanton effects.

Abstract

Based on Generalized Bloch equation the trans-series expansion for the phase (exponent) of the ground state density for double-well potential is constructed. It is shown that the leading and next-to-leading semiclassical terms are still defined by the flucton trajectory (its classical action) and quadratic fluctuations (the determinant), respectively, while the the next-to-next-to-leading correction (at large distances) is of non-perturbative nature. It comes from the fact that all flucton plus multi-instanton, instanton-anti-instanton classical trajectories lead to the same classical action behavior at large distances! This correction is proportional to sum of all leading instanton contributions to energy gap.