Metastability of (d+n)-dimensional elastic manifolds

TL;DR

This paper studies the quantum and thermal depinning of elastic manifolds in high-dimensional spaces, revealing a universal transition from quantum to classical behavior at a critical temperature.

Contribution

It introduces a universal analysis of depinning phenomena in elastic manifolds, identifying a sharp quantum-classical transition and deriving high-temperature asymptotics.

Findings

Identifies a sharp transition at temperature T_c from quantum to classical depinning.

Derives the Euclidean action behavior below and above T_c.

Provides high-temperature asymptotics for the preexponential factor in 1+1 dimensions.

Abstract

We investigate the depinning of a massive elastic manifold with $d$ internal dimensions, embedded in a $(d+n)$-dimensional space, and subject to an isotropic pinning potential $V({\bf u})=V(|{\bf u}|).$ The tunneling process is driven by a small external force ${\bf F}.$ We find the zero temperature and high temperature instantons and show that for the case $1\le d\le 6$ the problem exhibits a sharp transition from quantum to classical behavior: At low temperatures $T<T_{c}$ the Euclidean action is constant up to exponentially small corrections, while for $T> T_{c},$ ${S_{\rm Eucl}(d,T)}/{\hbar} = {U(d)}/{T}.$ The results are universal and do not depend on the detailed shape of the trapping potential $V({\bf u})$. Possible applications of the problem to the depinning of vortices in high-$T_{c}$ superconductors and nucleation in $d$-dimensional phase transitions are discussed. In addition, we determine the high-temperature asymptotics of the preexponential factor for the $(1+1)$-dimensional problem.