Continuum theory of vacancy-mediated diffusion

TL;DR

This paper develops a comprehensive continuum model for vacancy-mediated diffusion, capturing non-Gaussian tracer fluctuations across all dimensions and aligning with previous lattice results, while also extending to flux line fluctuations.

Contribution

It introduces a novel continuum theory for vacancy-driven diffusion applicable in all spatial dimensions, including extensions to flux line fluctuations.

Findings

Tracer fluctuations are strongly non-Gaussian.

Results agree with previous lattice calculations in integer dimensions.

Model extends to vacancy-driven flux line fluctuations.

Abstract

We present and solve a continuum theory of vacancy-mediated diffusion (as evidenced, for example, in the vacancy driven motion of tracers in crystals). Results are obtained for all spatial dimensions, and reveal the strongly non-gaussian nature of the tracer fluctuations. In integer dimensions, our results are in complete agreement with those from previous exact lattice calculations. We also extend our model to describe the vacancy-driven fluctuations of a slaved flux line.