The Asymmetric Avalanche Process

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 .

33 pages, 3 figures, revised version

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Cited by in corpus (27)

• Bethe Ansatz Solution of the Asymmetric Exclusion Process with Open Boundaries
• Universal cumulants of the current in diffusive systems on a ring
• Exact Spectral Gaps of the Asymmetric Exclusion Process with Open Boundaries
• Current fluctuations in the one dimensional Symmetric Exclusion Process with open boundaries
• On integrability of zero-range chipping models with factorized steady state
• Spectral theory for the q-Boson particle system
• Finite-time fluctuations for the totally asymmetric exclusion process
• Bethe ansatz solution of zero-range process with nonuniform stationary state
• Slowest relaxation mode of the partially asymmetric exclusion process with open boundaries
• Bethe ansatz solution of discrete time stochastic processes with fully parallel update
• Emergence of jams in the generalized totally asymmetric simple exclusion process
• Extrapolation methods and Bethe ansatz for the asymmetric exclusion process
• Class of solvable reaction-diffusion processes on Cayley tree
• Steady state of Stochastic Sandpile Models
• Current fluctuations and large deviations for periodic TASEP on the relaxation scale
• Transition from KPZ to Tilted Interface Critical Behavior in a Solvable Asymmetric Avalanche Model
• Directed abelian algebras and their applications to stochastic models
• Riemann surface for TASEP with periodic boundaries
• The transition probability and the probability for the left-most particle's position of the q-TAZRP
• The current distribution of the multiparticle hopping asymmetric diffusion model
• KPZ fluctuations in finite volume
• Transition Probabilities of the Bethe Ansatz Solvable Interacting Particle Systems
• Current statistics in the q-boson zero range process
• Multi-species extension of the solvable partially asymmetric reaction- diffusion processes
• Solvable multi-species reaction-diffusion processes, including the extended drop-push model
• Solvable multi-species reaction-diffusion processes, with particle-dependent hopping rates
• Crossover scaling functions in the asymmetric avalanche process