Driven Diffusion in Periodic Potentials with Stochastic Path Integral Hyperdynamics

TL;DR

This paper applies the Stochastic Path Integral Hyperdynamics method to study driven diffusion of particles in periodic potentials, revealing suppression of diffusion under certain conditions and demonstrating efficient extraction of dynamical data from simulations.

Contribution

It introduces the application of SPHD to analyze driven diffusion in periodic potentials, showing its effectiveness in extracting detailed dynamical information.

Findings

No stochastic resonance observed in single particle system.

Diffusion coefficient D is suppressed at higher frequencies.

Strong suppression of D occurs when dimer bond length is an integer multiple of lattice constant.

Abstract

We consider the driven diffusion of Brownian particles in 1D periodic potentials using the recently proposed Stochastic Path Integral Hyperdynamics (SPHD) scheme [L.Y. Chen and L.J.M. Horing, J. Chem. Phys. {\bf 126}, 224103 (2007)]. First, we consider the case where a single Brownian particle is moving in a spatially periodic potential and subjected to an external ac driving force. We confirm that there is no stochastic resonance in this system and find that at higher frequencies the diffusion coefficient $D$ is strongly suppressed. The second case is that of a dimer moving in a periodic potential with a static bias. For this case, there's a strong suppression of $D$ when the dimer bond length is an integer multiple of the lattice constant of the potential. For both cases, we demonstrate how the SPHD allows us to extract the dynamical information exactly at different bias levels from a single simulation run, by calculating the corresponding statistical re-weighting factors.