  We analyze quantal Brownian motion in $d$ dimensions using the unified model
for diffusion localization and dissipation, and Feynman-Vernon formalism. At
high temperatures the propagator possess a Markovian property and we can write
down an equivalent Master equation. Unlike the case of the
Zwanzig-Caldeira-Leggett model, genuine quantum mechanical effects manifest
themselves due to the disordered nature of the environment. Using Wigner
picture of the dynamics we distinguish between two different mechanisms for
destruction of coherence. The analysis of dephasing is extended to the low
temperature regime by using a semiclassical strategy. Various results are
derived for ballistic, chaotic, diffusive, both ergodic and non-ergodic motion.
We also analyze loss of coherence at the limit of zero temperature and clarify
the limitations of the semiclassical approach. The condition for having
coherent effect due to scattering by low-frequency fluctuations is also pointed
out. It is interesting that the dephasing rate can be either larger or smaller
than the dissipation rate, depending on the physical circumstances.
