Steady state of overdamped particles in the non-conservative force field of a simple non-linear model of optical trap

TL;DR

This paper provides an exact analytical solution for the steady state behavior of overdamped particles in a non-conservative force field typical of optical traps, including probability distributions and current circulations.

Contribution

It introduces the simplest non-conservative force model for optical traps and derives exact steady state statistics, advancing understanding of non-equilibrium particle dynamics.

Findings

Exact steady state probability distributions derived

Analytical expressions for probability currents and circulation

Numerical validation of analytical results

Abstract

Optically trapped particles are often subject to a non-conservative scattering force arising from radiation pressure. In this paper we present an exact solution for the steady state statistics of an overdamped Brownian particle subjected to a commonly used force field model for an optical trap. The model is the simplest of its kind that takes into account non-conservative forces. In particular, we present exact results for certain marginals of the full three dimensional steady state probability distribution as well as results for the toroidal probability currents which are present in the steady state, as well as for the circulation of theses currents. Our analytical results are confirmed by numerical solution of the steady state Fokker-Planck equation.