Tunneling and activated motion of a string across a potential barrier

A string in a potential barrier provides a conventional model for dislocations in crystals, charge-density waves in Peierls dielectrics, and the order-parameter phase in linear Josephson junctions. The joint effects of quantum tunneling and thermal activation result in a finite lifetime of the metastable states of the string. With exponential accuracy the decay rates for typical weakly asymmetric potentials and a cubic potential are calculated in the full temperature range. To do this, a new approach is proposed to calculate the decay rate in the crossover regions from the tunneling regime to that of activated tunneling and from the latter to the regime of thermal activation. The preexponential factor is calculated in the full temperature range except for a low-temperature region, where it changes only by a factor close to unity. For two typical potentials and a cubic potential the preexponential factors are plotted as functions of temperature. In the high-temperature regime the Arrhenius law holds with a universal temperature dependence of the preexponential factor, B∝$T^{\mathrm{-}1/2}$.