The harmonic approximation to single-file diffusion and its two-dimensional generalization

P. M. CENTRES; S. BUSTINGORRY

Workshop; LAWNP 2013; 2013

The single-le diusion is a paradigmatic problem in statistical physics, aimed to model the strictly one-dimensional diusion of particles with excluded volume interactions. It can be shown that, even in its simplest symmetric realization where forward and backward particle displacements occur with equal probability, the long time tagged particle diusion is subdiusive for innite systems. Within an harmonic approximation to particle interactions, this behavior can be traced back to the interface growing exponent related to the well known Edwards-Wilkinson equation where the diusion of the tagged particle is linked to the roughness of an interface model. Furthermore, it is well established that the asymmetric case can be associated to the Kardar-Parisi-Zhang equation. With this in mind, we take one step further and generalize this mapping to the two-dimensional case, where the single-le diusion condition is generalized not only by the excluded volume interaction but through the more stringent cage eect. This can be of key relevance to diusion models with constrained dynamics where the cage eect is an essential ingredient.