Metastability of(d+n)-dimensional elastic manifolds

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 $V(\mathbf{u})=V(|\mathbf{u}|).$ The tunneling process is driven by a small external force $\mathbf{F}.$ We find the zero-temperature and high-temperature instantons and show that for the case $1<~d<~6$ 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 $T>{T}_{c},$ ${S}_{\mathrm{Eucl}}(d,T)/\ensuremath{\Elzxh}=U(d)/T.$ The results are universal and do not depend on the detailed shape of the trapping potential $V(\mathbf{u}).$ 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.