Transport and diffusion of Brownian particles in a tilted deformable potential

The underdamped Brownian motion of particles in a deformable potential in response to a constant external force is investigated. Using the matrix continued fraction method, we compute the diffusion coefficient of Brownian particles via the dynamics factor structure at low temperature and intermediate values of friction coefficient. It is numerically found that the transport properties of Brownian particles such as the effective diffusion coefficient, the average velocity and the distribution probability are sensitive to the shape parameter r of the modified nonsinusoidal Remoissenet–Peyrard deformable potential. The bistable behaviour and the distribution of velocity which also shed light on the diffusion anomalies are discussed for some values of the shape parameter. We show that for the negative values of the shape parameter (r<0), the average velocity versus the external tilting of Brownian particles is optimized, while for the positive values (r>0), the average velocity of Brownian particles collapses due to the geometry of the system combined with the friction. Finally, the mechanism of enhancement of the effective diffusion coefficient for a range of the external force is discussed as a function of the shape parameter. We find a power law for the effective diffusion coefficient in terms of the shape parameter r, and show that, it evolves as D_th∼∣r∣².