Quantum Brownian transport in a correlated Gaussian force

Abstract

We study a classical system-bath model in which a system particle is linearly coupled to a bath of harmonic oscillators. In a system subject to white and correlated Gaussian noises, we derive an expression for the joint probability density, and the mean squared values of the system-bath particles are calculated. For white noise, the mean squared values of the system-bath particles exhibit an anomalous time dependence, which is different from that of normal diffusion. In particular, for a correlated Gaussian noise, the mean squared displacement and mean squared velocity of the bath particle show superspreading growths of $t^5$ and $t^3$ in $t{\ll}τ$, respectively. When $τ=0$, the mean squared velocity of a quantum particle under random noise is proportional to $t$, while the mean squared velocity of a bath particle in the presence of correlated Gaussian noise increases in proportion to $t^2$. This anomalous transport phenomenon results from the mixed derivative structure of the master equation, which couples with the transport coordinates in the diffusion dynamics of the relative coordinates. This result shows that the removal of dissipation in the Caldeira-Leggett framework leads to fundamentally different transport mechanisms characterized by non-diffusive quantum diffusion.