Diffusive transport is characterized by the scaling law ${\left(\text{length}\right)}^2\propto \left(\text{time}\right)$. In this paper we show that this relationship is significantly altered in curved analog spacetimes. This circumstance provides an opportunity to tailor diffusion: by a suitable design of the analog 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 analogs, curved graphene sheets, and so on (indeed with any analog spacetime).

• Received 19 December 2011

DOI:https://doi.org/10.1103/PhysRevE.85.041134