Quantum Brownian motion in a general environment: II nonlinear coupling and perturbative approach

BEI LOK HU; JUAN PABLO PAZ; YUHONG ZHANG

PHYSICAL REVIEW D - PARTICLE AND FILDS

AIP

Lugar: NEW YORK; Año: 1993 vol. 47 p. 1576 - 1590

0556-2821

We develop a perturbation scheme to treat the dynamics of a quantum Brownian particle (coordinate x) coupled nonlinearly to a bath of oscillators (coordinates qn) with an interaction action in the form λf(x)qnk. We derive the influence functionals for the k=2, 3, 4 cases to order λ2 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.