Asymmetric Simple Exclusion Process on a Cayley Tree

TL;DR

This paper analyzes the asymmetric exclusion process on a Cayley tree, revealing a single-phase steady state with flow properties independent of exit rates, highlighting implications for biological and fluid circulation systems.

Contribution

It introduces a new model of ASEP on a Cayley tree with arbitrary coordination, showing unique phase behavior and flow characteristics.

Findings

Steady state current is independent of exit rate.

Flow increases with entry rate and coordination number.

The model exhibits only one phase with no boundary layers.

Abstract

We study the asymmetric exclusion process on a regular Cayley tree with arbitrary co-ordination number. In this model particles can enter the system only at the parent site and exit from one of the sites at the last level. In the bulk they move from the occupied sites to one of their unoccupied downward neighbours, chosen randomly. We show that the steady state current that flow from one level to the next is independent of the exit rate, and increase monotonically with the entry rate and the co-ordination number. Unlike TASEP, the model has only one phase and the density profile show no boundary layers. We argue that in blood, air or water circulations systems branching is essential to maintain a free flow within the system which is independent of exit rates.