Metastability of (d+n)-dimensional elastic manifolds

Details Metastability of (d+n)-dimensional elastic manifolds Metastability of (d+n)-dimensional elastic manifolds

1998-09-09

arxiv.org/abs/cond-mat/9809141v1

Phys. Rev. B 58 (1998) 5486

Physics

Condensed Matter

Superconductivity

RevTeX, 10 pages, 3 figures inserted

Scientific paper

10.1103/PhysRevB.58.5486

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 $T T_{c},$ ${S_{\rm Eucl}(d,T)}/{\hbar} = {U(d)}/{T}.$ 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.

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