The Asymmetric Avalanche Process

TL;DR

This paper introduces an asymmetric stochastic model for avalanche dynamics on a ring, using Bethe ansatz to analyze flow properties, revealing a phase transition and universal behavior in particle flow statistics.

Contribution

It develops a kinetic equation incorporating exclusion and avalanche processes and applies Bethe ansatz to derive flow characteristics, including phase transition and universal large deviation functions.

Findings

Identified a phase transition from intermittent to continuous flow.

Derived the generating function and average velocity of particles.

Found the large deviation function has a universal form for the KPZ class.

Abstract

An asymmetric stochastic process describing the avalanche dynamics on a ring is proposed. A general kinetic equation which incorporates the exclusion and avalanche processes is considered. The Bethe ansatz method is used to calculate the generating function for the total distance covered by all particles. It gives the average velocity of particles which exhibits a phase transition from an intermittent to continuous flow. We calculated also higher cumulants and the large deviation function for the particle flow. The latter has the universal form obtained earlier for the asymmetric exclusion process and conjectured to be common for all models of the Kardar-Parisi-Zhang universality class .