Physics – Condensed Matter – Statistical Mechanics
Scientific paper
1997-08-07
Phys. Rev. B 56 (1997) 3130
Physics
Condensed Matter
Statistical Mechanics
14 pages, revtex, 9 figures inserted
Scientific paper
10.1103/PhysRevB.56.3130
The decay rate of metastable states is determined at high temperatures by thermal activation, whereas at temperatures close to zero quantum tunneling is relevant. At some temperature $T_{c}$ the transition from classical to quantum-dominated decay occurs. The transition can be first-order like, with a discontinuous first derivative of the Euclidean action, or smooth with only a second derivative developing a jump. In the former case the crossover temperature $T_{c}$ cannot be calculated perturbatively and must be found as the intersection point of the Euclidean actions calculated at low and high temperatures. In this paper we present a sufficient criterion for a first-order transition in tunneling problems and apply it to the problem of the tunneling of strings. It is shown that the problem of the depinning of a massive string from a linear defect in the presence of an arbitrarily strong dissipation exhibits a first-order transition.
Blatter Gianni
Gorokhov Denis A.
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