Dimer diffusion in a washboard potential

The transport of a dimer, consisting of two Brownian particles bounded by a harmonic potential, moving on a periodic substrate is investigated both numerically and analytically. The mobility and diffusion of the dimer center of mass present distinct properties when compared with those of a monomer under the same transport conditions. Both the average current and the diffusion coefficient are found to be complicated nonmonotonic functions of the driving force. The influence of dimer equilibrium length, coupling strength, and damping constant on the dimer transport properties are also examined in detail.

Figure 1

(Color online) Mobility (a) and diffusion coefficient (b) versus the dimer length $a_0$ for different values of the tilting force $F$. Simulation parameters: coupling constant $K=1.5$, temperature $T=0.1$, and $\gamma =1$. $D_{\infty }$ is the free diffusion coefficient of the dimer, $D_{\infty }=D_0\left(T/2\right)$; see text.

Figure 2

(Color online) Dimer configurations corresponding to zero pinning force and maximum diffusion coefficient; see also Fig. 1 and text.

Figure 3

(Color online) Diffusion coefficient $D$ versus the tilting force $F$ for a dimer length $a_0/L=1$ and different coupling constants $K$; $T=0.1$ and $\gamma =1$. The corresponding curves for monomers of temperature $T$ (solid, black) and $T/2$ (solid, red) are drawn for comparison (see text).

Figure 4

(Color online) Mobility (a) and diffusion coefficient (b) versus the tilting force $F$ for an equilibrium distance $a_0/L=1.5$ and for different values of the coupling constant $K$; $T=0.1$ and $\gamma =1$. In both panels the results are compared with the corresponding monomer curves (see text).

Figure 5

(Color online) Mobility (a) and diffusion coefficient (b) versus the tilting force $F$ for a coupling constant $K=1.5$ and for different values of the equilibrium distance $a_0$. $T$ and $\gamma$ have the same values as in Figs. 4, 3.

Figure 6

(Color online) Mobility (a) and diffusion coefficient (b) versus the tilting force $F$ for $a_0/L=1.5$ and different values of damping constant $\gamma$; $T=0.1$ and $K=0.3$. Two-peaked diffusion curves are clearly distinguishable for $\gamma \le 1$ only.