Towards an understanding of escape rate and state dependent diffusion for a quantum dissipative system
We address the stochastic dynamics of an open quantum system coupled to a heat reservoir that is driven out of thermal equilibrium by an external noise. By constructing Langevin and Fokker-Planck equations, we obtain the rate of decay from a metastable state of the system when the dissipation is state dependent. We discuss the effects and consequences of the non-linear interaction(s) stemming out of the system-bath coupling alongside the modulation of the bath by an external noise on the rate expression. We demonstrate that the temperature dependence of the escape rate is not only embedded in the so-called Arrhenius type factor, the second exponential factor also includes the temperature dependence. The last effect has a purely quantum origin. Interestingly, we also envisage that this quantum effect is entangled with dissipation. The results offer a basis for clarifying the relationship between the dissipation and exponential factor of the obtained rate expression.