Diffusion in periodic potentials with path integral hyperdynamics
Abstract
We consider the diffusion of Brownian particles in onedimensional periodic potentials as a test bench for the recently proposed stochastic path integral hyperdynamics (PIHD) scheme [Chen and Horing, J. Chem. Phys.JCPSA60021960610.1063/1.2737454 126, 224103 (2007)]. First, we consider the case where PIHD is used to enhance the transition rate of activated rare events. To this end, we study the diffusion of a single Brownian particle moving in a spatially periodic potential in the highfriction limit at low temperature. We demonstrate that the boost factor as compared to straight molecular dynamics (MD) has nontrivial behavior as a function of the bias force. Instead of growing monotonically with the bias, the boost attains an optimal maximum value due to increased error in the finite path sampling induced by the bias. We also observe that the PIHD method can be sensitive to the choice of numerical integration algorithm. As the second case, we consider parallel resampling of multiple bias force values in the case of a Brownian particle in a periodic potential subject to an external ac driving force. We confirm that there is no stochastic resonance in this system. However, while the PIHD method allows one to obtain data for multiple values of the ac bias, the boost with respect to MD remains modest due to the simplicity of the equation of motion in this case.
 Publication:

Physical Review E
 Pub Date:
 August 2011
 DOI:
 10.1103/PhysRevE.84.026703
 Bibcode:
 2011PhRvE..84b6703I
 Keywords:

 05.10.Gg;
 05.40.Jc;
 87.15.Vv;
 Stochastic analysis methods;
 Brownian motion;
 Diffusion