Current reversals of coupled driven and damped particles evolving in a tilted potential landscape

We explore the driven and damped dynamics of two coupled particles evolving in a symmetric and periodic substrate potential that is subjected to a static bias force. In addition, each particle is time-periodically driven with the same magnitude as, but out of phase to, its counterpart. It is shown that, for a certain parameter regime, the coupled particles can become self-organized and go against the direction of the bias force. This self-organization involves the particles becoming frequency locked with the driving force, and thus periodic motion ensues. We employ numerical arguments to show that running periodic states provide solutions of the system. Further, heuristic evidence is provided explaining how the two particles can travel against the bias force. In an effort to unearth coupling phenomena within the system, a detailed analysis of how the coupling strength affects the nonlinear dynamics is carried out. We show that within a range of coupling strengths the existence of periodic running solutions associated with negative mobility. To examine the robustness of our results we compare the deterministic system with the corresponding Langevin system. It is shown that, below a critical temperature, the qualitative behavior of the system remains the same.

Figure 1

Snapshots of the dimer motion against the bias force taken over a period $T$ of the external time-periodic modulation. Arrows indicate direction and magnitude of a particle's momentum. Left (right): particle 1 (particle 2). Here $F_0=0.1$, $\gamma =0.11$, $F=1.3$, $\Omega =2.22$, ${\theta }_0=0$, and $\kappa =0.372$.

Figure 2

Time evolution, omitting an initial transient, of the mean velocity in the presence of a heat bath of thermal energy $k_{B}T={10}^{-3}\Delta E$, with $\Delta E=1/\pi$ being the energetic barrier height of the washboard potential. The system parameters are given in Fig. 1.

Figure 3

Bifurcation diagram as a function of the coupling parameter $\kappa$. The remaining parameters are given in Fig. 1.

Figure 4

The current, as defined in Sec. 4, as a function of the coupling parameter $\kappa$. The remaining parameters are given in Fig. 1. The blue dashed line serves to highlight the regions of negative current.

Figure 5

(top) Time evolution of the two uncoupled particles ($\kappa =0$), traveling with the bias force. (bottom) Time evolution of the two coupled particles ($\kappa =0.327$) that are traveling in the opposite direction to the bias force. The two lines represent the trajectories of the individual particles. The system parameters are given in Fig. 1. Note the different time scales.