Saddle-point approximation to the false vacuum decay at finite temperature in one-dimensional quantum mechanics

TL;DR

This paper develops a saddle-point approximation method to calculate the false vacuum decay rate at finite temperature in one-dimensional quantum mechanics, extending zero-temperature results and analyzing temperature effects.

Contribution

It introduces finite-temperature bounce solutions and compares the decay rate with previous zero-temperature and finite-temperature results, providing new insights into thermal effects on vacuum decay.

Findings

Finite-temperature bounce solutions are derived and analyzed.

Decay rate increases with temperature, consistent with theoretical predictions.

Numerical results illustrate the temperature dependence of the decay rate.

Abstract

We calculate the false-vacuum decay rate in one-dimensional quantum mechanics on the basis of the saddle-point approximation in the Euclidean path integral at finite temperature. The saddle points are the finite-T and shifted bounce solutions, which are finite-period analogs of the (zero-temperature) bounce solution, and the shot solutions. We re-examined the zero-temperature result by Callan and Coleman and compare with the zero-temperature limit of our results. We also perform some numerical calculations to illustrate the temperature dependence of the decay rate and compare it with the result by Affleck.