Observing Quantum Tunneling in Perturbation Series

TL;DR

This paper demonstrates that Borel resummation of perturbation series can accurately capture quantum tunneling effects by reproducing the imaginary part of energy eigenvalues in a metastable potential, aligning well with exact numerical results.

Contribution

It introduces a numerical application of Borel resummation to connect perturbation series with tunneling phenomena in quantum mechanics.

Findings

Borel transform discontinuity reproduces the imaginary energy component.

High agreement between resummation results and exact numerical values.

Effective in the entire tunneling regime for 0<g≤0.7.

Abstract

We apply Borel resummation method to the conventional perturbation series of ground state energy in a metastable potential, $V(x)=x^2/2-gx^4/4$. We observe numerically that the discontinuity of Borel transform reproduces the imaginary part of energy eigenvalue, i.e., total decay width due to the quantum tunneling. The agreement with the exact numerical value is remarkable in the whole tunneling regime $0<g\lsim0.7$.