The effect of Magnetic Field on MQT Escape Time in "Small" Josephson Junctions

We study the phenomenon of macroscopic quantum tunneling (MQT) in a finite size Josephson junction (JJ) with an externally applied magnetic field. As it is well known, the problem of MQT in a point-like JJ is reduced to the study of the under-barrier motion of a quantum particle in the washboard potential. In the case of a finite size JJ placed in magnetic field, this problem is considerably more complex since, besides the phase, the potential itself, depends on space variables. We find the general expressions both for the crossover temperature $T_{0}$ between thermally activated and macroscopic quantum tunneling regimes and the escape time $\tau_{\mathrm{esc}}$. It turns out that in proximity of particular values of magnetic field the crossover temperature can vary non-monotonically.