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We derive and solve analytically the non-Markovian master equation forharmonic quantum Brownian motion proving that, for weak system-reservoircouplings and high temperatures, it can be recast in the form of the masterequation for a harmonic oscillator interacting with a squeezed thermal bath.This equivalence guarantees preservation of positivity of the density operatorduring the time evolution and allows one to establish a connection between thedynamics of Schr\"odinger cat states in squeezed environments andenvironment-induced decoherence in quantum Brownian motion.

the european physical journal. d, atomic, molecular and optical physics/the european physical journal. d, atomic, molecular, optical and plasma physics

Non-Markovian weak coupling limit of quantum Brownian motion