Quantum and Thermal Depinning of a String from a Linear Defect

TL;DR

This paper analyzes the decay of an elastic string from a linear defect under small forces, calculating decay rates using instanton methods and exploring a transition from quantum tunneling to thermal activation.

Contribution

It introduces a detailed calculation of decay rates for a string depinning problem, incorporating fluctuations and identifying a first order transition between quantum and thermal regimes.

Findings

Decay rate calculated with instanton method

Transition from quantum tunneling to thermal activation

Model applicable to nucleation in quantum phase transitions

Abstract

The problem of a massive elastic string depinning from a linear defect under the action of a small driving force is considered. To exponential accuracy the decay rate is calculated with the help of the instanton method; then, fluctuations of the quasiclassical solution are taken into account to determine the preexponential factor. The decay rate exhibits a kind of first order transition from quantum tunneling to thermal activation with vanishing crossover region. The model may be applied to describe nucleation in 2-dimensional first order quantum phase transitions.