  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 vanishing
crossover region. The model may be applied to describe nucleation in
2-dimensional first order quantum phase transitions.
