Generalized Langevin dynamics simulation with non-stationary memory kernels: How to make noise

TL;DR

This paper introduces a numerical method to simulate non-stationary generalized Langevin dynamics by replacing deterministic forces with stochastic processes, enabling accurate coarse-grained modeling of driven microscopic systems.

Contribution

It provides a novel approach to generate stochastic forces for non-stationary memory kernels in generalized Langevin equations, facilitating coarse-grained simulations of time-dependent systems.

Findings

Method accurately reproduces observable distributions up to specified moments.

Enables simulation of driven processes with non-stationary memory effects.

Integrates with kernel extraction techniques for microscopic data.

Abstract

We present a numerical method to produce stochastic dynamics according to the generalized Langevin equation with a non-stationary memory kernel. This type of dynamics occurs when a microscopic system with an explicitly time-dependent Liouvillian is coarse-grained by means of a projection operator formalism. We show how to replace the deterministic fluctuating force in the generalized Langevin equation by a stochastic process, such that the distributions of the observables are reproduced up to moments of a given order. Thus, in combination with a method to extract the memory kernel from simulation data of the underlying microscopic model, the method introduced here allows to construct and simulate a coarse-grained model for a driven process.