Nonlinear coupling mechanism in a quantum system

For a quantum system coupled to a heat bath environment the nonlinear dissipation is studied starting from imaginary-time path-integral formulation. An effective classical potential (ECP) is obtained in which not only the frequency of the potential but also the slope of the coupling form factor are treated as trial functions, they are determined by minimizing the effective classical potential. Further, terms of higher order are also added in an improved Gaussian measure in order to regularize integrals of fluctuation modes at low temperatures. Various approximations to thermodynamic functions of a double-well potential are compared with the dissipative path-integral Monte Carlo method. In particular, it occurs for single- or double-well potentials, where nonlinear dissipation can induce the appearance of multistable states and barrier drift. Nonmonotonic varying of the barrier height of the ECP with temperature is found in a bistable system.