From Generalized Langevin Equations to Brownian Dynamics and Embedded Brownian Dynamics

Abstract

We present the reduction of generalized Langevin equations to a coordinate-only stochastic model, which in its exact form, involves a forcing term with memory and a general Gaussian noise. It will be shown that a similar fluctuation-dissipation theorem still holds at this level. We study the approximation by the typical Brownian dynamics as a first approximation. Our numerical test indicates how the intrinsic frequency of the kernel function influences the accuracy of this approximation. In the case when such an approximate is inadequate, further approximations can be derived by embedding the nonlocal model into an extended dynamics without memory. By imposing noises in the auxiliary variables, we show how the second fluctuation-dissipation theorem is still exactly satisfied.

28 pages, 8 figures

References in corpus (2)

• Data-driven parameterization of the generalized Langevin equation
• The Derivation and Approximation of Coarse-grained Dynamics from Langevin Dynamics

Cited by in corpus (5)

• Dynamics of Current, Charge and Mass
• Model reduction techniques for the computation of extended Markov parameterizations for generalized Langevin equations
• Atomistic simulation of martensite microstructural evolution during temperature driven $\beta \to \alpha$ transition in pure titanium
• Electrodynamics Correlates Knock-on and Knock-off: Current is Spatially Uniform in Ion Channels
• Brownian dynamics of Dirac fermions in twisted bilayer graphene