An exact sampling scheme for Brownian motion in the presence of a magnetic field

TL;DR

This paper presents an exact sampling scheme for simulating Brownian motion of charged particles under a magnetic field, solving the Langevin equation with correlated variables.

Contribution

It introduces a novel exact sampling method for position and velocity components in magnetic field-influenced Brownian motion.

Findings

Exact sampling scheme successfully implemented.

Handles correlated random variables in the Langevin equation.

Applicable to diffusion of charged particles in magnetic fields.

Abstract

Langevin equation pertinent to diffusion limited aggregation of charged particles in the presence of an external magnetic field is solved exactly. The solution involves correlated random variables. A new scheme for exactly sampling the components of the position and velocity is proposed.