# Driven anisotropic diffusion at boundaries: noise rectification and particle sorting

## TL;DR

This paper reveals how anisotropic thermal environments near surfaces can induce directed particle motion through noise rectification, enabling particle sorting without external forces.

## Contribution

It provides an exact solution to the Fokker-Planck equation for anisotropic diffusion near boundaries and proposes an experimental setup for observing noise-induced transport and particle sorting.

## Key findings

- Directed transport occurs without external forces due to anisotropic diffusion.
- The mechanism enables sorting particles based on size and properties.
- Theoretical predictions are supported by a proposed experimental design.

## Abstract

We study the diffusive dynamics of a Brownian particle in proximity of a flat surface under non-equilibrium conditions, which are created by an anisotropic thermal environment with different temperatures being active along distinct spatial directions. By presenting the exact time-dependent solution of the Fokker-Planck equation for this problem, we demonstrate that the interplay between anisotropic diffusion and hard-core interaction with the plain wall rectifies the thermal fluctuations and induces directed particle transport parallel to the surface, without any deterministic forces being applied in that direction. Based on current micromanipulation technologies, we suggest a concrete experimental set-up to observe this novel noise-induced transport mechanism. We furthermore show that it is sensitive to particle characteristics, such that this set-up can be used for sorting particles of different size.