Exact results for an asymmetric annihilation process with open boundaries

Abstract

We consider a nonequilibrium reaction-diffusion model on a finite one dimensional lattice with bulk and boundary dynamics inspired by Glauber dynamics of the Ising model. We show that the model has a rich algebraic structure that we use to calculate its properties. In particular, we show that the Markov dynamics for a system of a given size can be embedded in the dynamics of systems of higher sizes. This remark leads us to devise a technique we call the transfer matrix Ansatz that allows us to determine the steady state distribution and correlation functions. Furthermore, we show that the disorder variables satisfy very simple properties and we give a conjecture for the characteristic polynomial of Markov matrices. Lastly, we compare the transfer matrix Ansatz used here with the matrix product representation of the steady state of one-dimensional stochastic models.

18 pages

References in corpus (6)

• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• The asymmetric simple exclusion process: an integrable model for non-equilibrium statistical mechanics
• Matrix representation of the stationary measure for the multispecies TASEP
• Matrix product solution of the multispecies partially asymmetric exclusion process
• Injected Power Fluctuations in 1D Dissipative Systems

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• Hydrodynamic equations for space-inhomogeneous aggregating fluids with first-principle kinetic coefficients
• Coverage fluctuations in theater models
• Transfer matrices for the totally asymmetric exclusion process
• Assortative Exchange Processes
• Aggregation Driven by a Localized Source
• Lattice SUSY for the DiSSEP at ${\lambda }^2=1$ (and ${\lambda }^2=-3$)