Decay of Metastable States: Sharp Transition from Quantum to Classical Behavior

TL;DR

This paper investigates the transition from quantum to classical decay of metastable states, identifying conditions for first-order transitions and applying the theory to string tunneling with dissipation.

Contribution

It provides a criterion for first-order quantum-classical transitions and demonstrates its application to string depinning problems with dissipation.

Findings

First-order transition occurs in string depinning with dissipation.

Transition criterion applicable to tunneling problems.

Depinning of a massive string exhibits a first-order transition.

Abstract

The decay rate of metastable states is determined at high temperatures by thermal activation, whereas at temperatures close to zero quantum tunneling is relevant. At some temperature $T_{c}$ the transition from classical to quantum-dominated decay occurs. The transition can be first-order like, with a discontinuous first derivative of the Euclidean action, or smooth with only a second derivative developing a jump. In the former case the crossover temperature $T_{c}$ cannot be calculated perturbatively and must be found as the intersection point of the Euclidean actions calculated at low and high temperatures. In this paper we present a sufficient criterion for a first-order transition in tunneling problems and apply it to the problem of the tunneling of strings. It is shown that the problem of the depinning of a massive string from a linear defect in the presence of an arbitrarily strong dissipation exhibits a first-order transition.