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 $1\le d\le 6$ 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 $T>T_c,$ $S_{\mathrm{Eucl}}(d,T)/\hslash =U(d)/T.$ 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.

RevTeX, 10 pages, 3 figures inserted

References in corpus (3)

• First- and Second-Order Transitions between Quantum and Classical Regimes for the Escape Rate of a Spin System
• Decay of Metastable States: Sharp Transition from Quantum to Classical Behavior
• Thermally activated Hall creep of flux lines from a columnar defect

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