Collective Mode Brownian Dynamics: A Method for Fast Relaxation of Statistical Ensembles

It can be challenging to sample equilibrium configurations of correlated systems of particles with slow relaxation times (e.g., polymeric systems) using conventional molecular dynamics and Monte Carlo methods. This is especially true for systems with complicated, extended bond network topologies and other interactions that make the use and design of specialized relaxation protocols infeasible. We introduce a method based on Brownian dynamics (BD) simulations that can reduce the computational time it takes to reach equilibrium and measure decorrelated samples. Importantly, the method is completely agnostic to particle configuration and the specifics of interparticle forces. In particular, we develop a mobility matrix that excites non-local, collective motion of N particles and can be computed efficiently in O(N) time. Particle motion is integrated according to the overdamped Langevin equation with hydrodynamic interactions, where Brownian displacements are drawn efficiently using a split representation of the mobility matrix in position and wave space. We demonstrate the efficacy of the method with various examples from the realm of soft condensed matter.