Exactly solvable model of dissipative vortex tunneling

I consider the problem of vortex tunneling in a two-dimensional superconductor. The vortex dynamics is governed by the Magnus force and the Ohmic friction force. Under-barrier motion in the vicinity of the saddle point of the pinning potential leads to a model with quadratic Hamiltonian which can be analytically diagonalized. I find the dependence of the tunneling probability on the normal state quasiparticle relaxation time $\tau$ with a minimum at ${\omega }_0\tau \sim 1$, where ${\omega }_0$ is the level spacing of the quasiparticle bound states inside the vortex core. The results agree qualitatively with the available experimental data.