Tunneling in a Time Dependent Setting

TL;DR

This paper introduces a novel algorithm combining WKB and complex time path methods to analyze tunneling processes in various time-dependent physical systems where standard techniques fail.

Contribution

It presents a new computational approach for tunneling in time-dependent settings, applicable to problems like topological defect nucleation, particle pair production, and false vacuum decay.

Findings

Calculated decay rates for particle-antiparticle pair production

Analyzed false vacuum decay in oscillating initial states

Demonstrated method's applicability to diverse time-dependent tunneling problems

Abstract

A standard approach to analyzing tunneling processes in various physical contexts is to use instanton or imaginary time path techniques. For systems in which the tunneling takes place in a time dependent setting, the standard methods are often applicable only in special cases, e.g. due to some additional symmetries. We consider a collection of time dependent tunneling problems to which the standard methods cannot be applied directly, and present an algorithm, based on the WKB approximation combined with complex time path methods, which can be used to calculate the relevant tunneling probabilities. This collection of problems contains, among others, the spontaneous nucleation of topological defects in an expanding universe, the production of particle - antiparticle pairs in a time dependent electric field, and false vacuum decay in field theory from a coherently oscillating initial state. To demonstrate the method, we present detailed calculations of the time dependent decay rates for the last two examples.