Thermorelaxation resonance in the quantum theory of Brownian motion

The Brownian motion of a quantum particle in a thermal reservoir possessing a finite correlation time $\tau_c$ is considered. Non-Markov Langevin equations for a stationary nonequilibrium state are obtained. At low temperatures $T$ of the thermal reservoir, the correlation time $\tau_c=\hbar/2\pi T$ is fairly long. It is shown that allowance for the damping $\gamma$ of the particle momentum over the correlation times $\tau_c$: $\gamma\tau_c\simeq1$, leads to an oscillating temperature dependence of the relaxation coefficient $\gamma(1/T)$ in the region of low temperatures of the thermal reservoir.