Nonequilibrium master equation for interacting Brownian particles in a deep-well periodic potential

Noise-cancellation algorithm for simulations of Brownian particles

We investigate the usage of a recently introduced noise-cancellation algorithm for Brownian simulations to enhance the precision of measuring transport properties such as the mean-square displacement or the velocity-autocorrelation function. The algorithm is based on explicitly storing the pseudorandom numbers used to create the randomized displacements in computer simulations and subtracting them from the simulated trajectories. The resulting correlation function of the reduced motion is connected to the target correlation function up to a cross-correlation term. Using analytical theory and computer simulations, we demonstrate that the cross-correlation term can be neglected in all three systems studied in this paper. We further expand the algorithm to Monte Carlo simulations and analyze the performance of the algorithm and rationalize that it works particularly well for unbounded, weakly interacting systems in which the precision of the mean-square displacement can be improved by orders of magnitude.

Gutzwiller approximation for indistinguishable interacting Brownian particles on a lattice

Nonequilibrium Brownian systems can be described using a creation and annihilation operator formalism for classical indistinguishable particles. This formalism has recently been used to derive a many-body master equation for Brownian particles on a lattice with interactions of arbitrary strength and range. One advantage of this formalism is the possibility of using solution methods for analogous many-body quantum systems. In this paper, we adapt the Gutzwiller approximation for the quantum Bose-Hubbard model to the many-body master equation for interacting Brownian particles in a lattice in the large-particle limit. Using the adapted Gutzwiller approximation, we numerically explore the complex behavior of nonequilibrium steady-state drift and number fluctuations throughout the full range of interaction strengths and densities for on-site and nearest-neighbor interactions.