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 in an 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.