Title: "General Quantum Brownian Motion with Initially Correlated and Nonlinearly Coupled Environment"
The linear-coupling models of Quantum Brownian Motion have
been repeatedly analyzed because of there being technically tractable
and as they provide a good approximation to a number of physical situations.
However, in many problems of interest in physics notably in field theory and
gravitation there is some form of nonlinearity between the system and its
environment. With this aim in view and also because of its technical interest
we analyze the problem of nonlinear Quantum Brownian Motion with correlated
initial conditions. We obtain the Influence Functional for the system
perturbatively for quadratic coupling in the environmental variables and apply
it to obtain the propagator when the particle is in a harmonic as well as when
additional anharmonic 'Washboard' potential. For the harmonic potential
case, we obtain the master equation and the Wigner equation for the generalized
initial condition as well as for the simpler 'thermal' initial condition and
establish the corresponding fluctuation-dissipation theorem.