Metastability of (d+n)-dimensional elastic manifolds

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(u) = V(/u/). The tunneling process is driven by a small external force F. We find the zero-temperature and high-temperature instantons and show that for the case 1 less than or equal to d less than or equal to 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-Eucl(d,T)/(h) over bar = U(d)/T. The results are universal and do not depend on the detailed shape of the trapping potential V(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.