QUANTUM BROWNIAN-MOTION IN A GENERAL ENVIRONMENT .2. NONLINEAR COUPLING AND PERTURBATIVE APPROACH

We develop a perturbation scheme to treat the dynamics of a quantum Brownian particle (coordinate x) coupled nonlinearly to a bath of oscillators (coordinates q(n)) with an interaction action in the form lambdaf(x)q(n)k. We derive the influence functionals for the k = 2,3,4 cases to order lambda2 and derive the master equations for the special cases of local dissipation and white noise, as well as the general cases of nonlocal dissipation and colored noise for f(x) = x and x2. We show that a generalized fluctuation-dissipation relation exists between the lth-order noise kernels of the kth-order coupling and their corresponding dissipation kernels.