Accurate sampling using Langevin dynamics

TL;DR

This paper introduces a simple integrator for Langevin dynamics that accurately samples distributions, even in high-friction regimes, and demonstrates its effectiveness through practical simulations of a Lennard-Jones crystal.

Contribution

It presents a novel, simple integrator for Langevin equations with on-the-fly accuracy checks, improving sampling reliability in challenging regimes.

Findings

Effective sampling in high-friction limit demonstrated

Integrator accuracy verified using effective energy concept

Practical application shown with Lennard-Jones crystal

Abstract

We show how to derive a simple integrator for the Langevin equation and illustrate how it is possible to check the accuracy of the obtained distribution on the fly, using the concept of effective energy introduced in a recent paper [J. Chem. Phys. 126, 014101 (2007)]. Our integrator leads to correct sampling also in the difficult high-friction limit. We also show how these ideas can be applied in practical simulations, using a Lennard-Jones crystal as a paradigmatic case.