A generalized Theory of Diffusion based on Kinetic Theory

TL;DR

This paper introduces spin hydrodynamics as a unified model for spin diffusion, bridging dense and dilute regimes, and demonstrates its effectiveness in describing spin relaxation in atomic gases.

Contribution

It presents spin hydrodynamics as a generalization of diffusion equations, applicable across different interaction regimes, and validates it against experimental data.

Findings

Spin hydrodynamics reduces to Fick's law in dense limits.

In dilute limits, it matches collisionless Boltzmann behavior.

Predicted diffusion constants agree with experimental measurements.

Abstract

We propose to use spin hydrodynamics, a two-fluid model of spin propagation, as a generalization of the diffusion equation. We show that in the dense limit spin hydrodynamics reduces to Fick's law and the diffusion equation. In the opposite limit spin hydrodynamics is equivalent to a collisionless Boltzmann treatment of spin propagation. Spin hydrodynamics avoids unphysical effects that arise when the diffusion equation is used to describe to a strongly interacting gas with a dilute corona. We apply spin hydrodynamics to the problem of spin diffusion in a trapped atomic gas. We find that the observed spin relaxation rate in the high temperature limit [Sommer et al., Nature 472, 201 (2011)] is consistent with the diffusion constant predicted by kinetic theory.