Directed motion in a periodic potential of a quantum system coupled to a heat bath driven by a colored noise

A system-reservoir nonlinear coupling model is proposed for a quantum system when the associated bath is not in thermal equilibrium but is modulated by an external colored noise, to present a microscopic approach to quantum state-dependent diffusion and multiplicative noise in terms of a quantum Langevin description. Consequently, the Fokker-Planck equation in position space, valid in the overdamped limit, for multiplicative colored noise is constructed to explore the possibility of observing a quantum current and dependence of the current on various parameters of external noise is examined.

Figure 1

Plot of effective potential $\left[\varphi \left(q\right)\right]$ with external noise strength $\left(D\right)=1.0$, correlation time of external noise $\left(\tau \right)=0.2$ and phase difference between coupling function and periodic potential $\left(\theta \right)=0.69\pi$.

Figure 2

Variation of current, $J$ with phase difference $\theta$ (in unit of $\pi$) for various $\tau$, where $D=1.0$.

Figure 3

Plot of current, $J$ as a function of phase difference, $\theta$ (in units of $\pi$) for different $D$, where $\tau =0.2$.

Figure 4

Plot of current $J$ as a function of $D$ for different $\tau$ values with $\theta =0.69\pi$.

Figure 5

Plot of current $J$ as a function of temperature $T$ for different $\tau$ values with $\theta =0.69\pi$ and $D=1.0$.