Phonon mode cooperating with a particle serving as a Maxwell gate and rectifier

A fully standard quantum model of a particle interacting with a single-mode phonon system under the influence of a thermodynamic bath is considered. Numerically exact solution shows that, for very specific values of parameters involved, the phonon mode cooperating with the particle becomes able to respond to particle hops and thus to suppress the back particle transfer. The particle becomes free at the end of the process, during which it can be transferred prevailingly in one direction only, even going uphill in energy, at the cost of just the thermal energy of the single bath. This behaviour is due to the fact that both the particle and the particle + oscillator density matrices differ, in the stationary situations and for at least intermediate oscillator coupling to the bath, from the respective canonical forms.