Tailoring diffusion in analogue spacetimes

TL;DR

This paper demonstrates that in curved analogue spacetimes, diffusive transport can be tailored to be faster or slower than normal, enabling customizable diffusion properties in various physical systems.

Contribution

It introduces the concept that the diffusion law can be significantly altered in curved analogue spacetimes through metric design, allowing for controlled diffusion rates.

Findings

Diffusion scaling law is modified in curved analogue spacetimes.

Designing the metric can tailor diffusion speed.

Potential experimental tests with optical and graphene analogues.

Abstract

Diffusive transport is characterized by the scaling law $(length)^{2}\propto(time)$. In this letter we show that this relationship is significantly altered in curved analogue spacetimes. This circumstance provides an opportunity to tailor diffusion: by a suitable design of the analogue metric, it is possible to create materials where diffusion is either faster or slower than in normal media, as desired. This prediction can in principle be tested experimentally with optical analogues, curved graphene sheets, etc. - indeed with any analogue spacetime.