Quantum and thermal depinning of a string from a linear defect

The problem of a massive elastic string depinning from a linear defect under the action of a small driving force is considered. To exponential accuracy the decay rate is calculated with the help of the instanton method; then, fluctuations of the quasiclassical solution are taken into account to determine the preexponential factor. The decay rate exhibits a kind of first-order transition from quantum tunneling to thermal activation with a vanishing crossover region. The model may be applied to describe nucleation in two-dimensional first-order quantum phase transitions.