### abstract

- A new model that generalizes the study of quantum Brownian motion (BM) is constructed. We consider disordered environment that may be either static (quenched), noisy or dynamical. The Zwanzig-Caldeira-Leggett BM-model constitutes formally a special case where the disorder auto-correlation length is taken to be infinite. Alternatively, localization problem is obtained if the noise auto-correlation time is taken to be infinite. Also the general case of weak nonlinear coupling to thermal, possibly chaotic bath is handled by the same formalism. A general, Feynman-Vernon type path-integral expression for the propagator is introduced. Wigner transformed version of this expression is utilized in order to facilitate comparison with the classical limit. It is demonstrated that non-stochastic genuine quantal manifestations are associated with the new model. It is clarified that such effects are absent in the standard BM model, either the disorder or the chaotic nature of the bath are essential. Quantal correction to the classical diffusive behavior is found even in the limit of high temperatures. The suppression of interference due to dephasing is discussed, leading to the observation that due to the disorder the decay of coherence is exponential in time, and no longer depends on geometrical considerations. Fascinating non-Markovian effects due to time-correlated (colored) noise are explored. For this, a new strategy is developed in order to handle the integration over paths. This strategy is extended in order to demonstrate how localization comes out from the path integral expression. Comment: LaTeX, 26 pages, 4 figures, errata included