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 a non-monotonic dependence of the tunneling probability on the friction coefficient with a maximum at tan ΘH ∼ 1, where ΘH is the Hall angle.