Quasi symplectic integrators for stochastic differential equations

TL;DR

This paper introduces two specialized quasi-symplectic algorithms for numerically integrating stochastic differential equations of Brownian motion, improving accuracy in equilibrium distribution reproduction and comparing favorably with existing methods.

Contribution

The paper presents novel quasi-symplectic integrators that become symplectic in certain limits and offer higher-order accuracy for equilibrium distributions.

Findings

Algorithms reproduce equilibrium distributions more accurately.

Comparisons show improved performance over existing schemes.

Effective for static and dynamical quantities.

Abstract

Two specialized algorithms for the numerical integration of the equations of motion of a Brownian walker obeying detailed balance are introduced. The algorithms become symplectic in the appropriate limits, and reproduce the equilibrium distributions to some higher order in the integration time step. Comparisons with other existing integration schemes are carried out both for static and dynamical quantities.