The Study of Shocks in Three-States Driven-Diffusive Systems: A Matrix Product Approach

Abstract

We study the shock structures in three-states one-dimensional driven-diffusive systems with nearest neighbors interactions using a matrix product formalism. We consider the cases in which the stationary probability distribution function of the system can be written in terms of superposition of product shock measures. We show that only three families of three-states systems have this property. In each case the shock performs a random walk provided that some constraints are fulfilled. We calculate the diffusion coefficient and drift velocity of shock for each family.

15 pages, Accepted for publication in Journal of Statistical Mechanics: Theory and Experiment (JSTAT)

References in corpus (7)

• Representations of the quadratic Algebra and Partially Asymmetric Diffusion with Open Boundaries
• Finite Dimensional Representations of the Quadratic Algebra: Applications to the Exclusion Process
• Microscopic structure of travelling wave solutions in a class of stochastic interacting particle systems
• Exact shock measures and steady-state selection in a driven diffusive system with two conserved densities
• Shocks in the asymmetric exclusion process with internal degree of freedom
• Matrix Product States of Three Families of One-Dimensional Interacting Particle Systems
• Multiple Shocks in a Driven Diffusive System with Two Species of Particles

Cited by in corpus (4)

• Dynamical Critical Exponent for Two-Species Totally Asymmetric Diffusion on a Ring
• Finite-dimensional representation of the quadratic algebra of a generalized coagulation-decoagulation model
• Multi-species reaction-diffusion models admitting shock solutions
• Relaxation time in a non-conserving driven-diffusive system with parallel dynamics