Estimating the diffusion coefficient of trapped particles

TL;DR

This paper introduces a method to estimate the free-space diffusion coefficient of trapped particles from equilibrium trajectories, providing accurate bounds and measurements applicable to various trapping potentials and weak interactions.

Contribution

The paper presents a novel approach to estimate the diffusion coefficient from equilibrium data, especially for harmonic traps, improving upon traditional non-equilibrium methods.

Findings

Estimates are asymptotically exact for harmonic traps.

The method provides a lower bound for generic trapping potentials.

Estimates remain accurate with weak interactions and anharmonicities.

Abstract

We show that observing the trajectories of confined particles in a thermal equilibrium state yields an estimate on the free-space diffusion coefficient. For generic trapping potentials and interactions between particles, the estimate comes in the form of a lower bound on the true diffusion coefficient. For non-interacting particles in harmonic trapping potentials, which approximately describes many experimental situations, the estimate is asymptotically exact. This allows to determine the diffusion coefficient from an equilibrium measurement, as opposed to a direct observation of diffusion, which necessarily starts from a non-equilibrium state. We explicitly demonstrate that the estimate remains quantitatively accurate in the presence of weak interactions and anharmonic corrections.