Brownian motion in an inhomogeneous medium has been
recently studied in the context of classical Brownian motion
(CBM) and other classical diffusive systems. Precisely, explicit
formulas were derived for noise-induced drifts in the
small-mass (Smoluchowski-Kramers and other limits).
In a series of papers we analyzed the microscopic
model of quantum Brownian motion, describing a Brown-
ian particle interacting with a bosonic thermal bath, through
a coupling which is linear in the creation and annihilation
operators of the bath, but may be a nonlinear function of
the position of the particle. Physically, this corresponds to a
configuration in which damping and diffusion are inhomogeneous,
namely they vary in space.
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