Bifurcation of Periodic Instanton in Decay-Rate Transition

TL;DR

This paper analyzes the bifurcation behavior of periodic instantons in quantum mechanical models, deriving a general condition for bifurcation points that enhances understanding of decay rate transitions.

Contribution

It introduces a new analytical condition for the appearance of bifurcation points in the action-temperature diagram, extending previous criteria.

Findings

Multiple zero modes occur at bifurcation points.

The derived condition predicts the number of bifurcation points.

Previous criteria are special cases of this general condition.

Abstract

We investigate a bifurcation of periodic instanton in Euclidean action-temperature diagram in quantum mechanical models. It is analytically shown that multiple zero modes of fluctuation operator should be arised at bifurcation points. This fact is used to derive a condition for the appearance of bifurcation points in action-temperature diagram. This condition enables one to compute the number of bifurcation points for a given quantum mechanical system and hence, to understand the whole behaviour of decay rate. It is explicitly shown that the previous criterion derived by nonlinear perturbation or negative-mode consideration is special limit of our case.