Theory of fractional vortex escape in a 0-kappa long Josephson junction

We consider a fractional Josephson vortex in an infinitely long 0-kappa Josephson junction. A uniform bias current applied to the junction exerts a Lorentz force acting on a vortex. When the bias current becomes equal to the critical (or depinning) current, the Lorentz force tears away an integer fluxon and the junction switches to the resistive state. In the presence of thermal and quantum fluctuations this escape process takes place with finite probability already at subcritical values of the bias current. We analyze the escape of a fractional vortex by mapping the Josephson phase dynamics to the dynamics of a single particle in a metastable potential and derive the effective parameters of this potential. This allows us to predict the behavior of the escape rate as a function of the topological charge of the vortex.