Solvable multi-species reaction-diffusion processes, with particle-dependent hopping rates

Abstract

By considering the master equation of the totally asymmetric exclusion process on a one-dimensional lattice and using two types of boundary conditions (i.e. interactions), two new families of the multi-species reaction-diffusion processes, with particle-dependent hopping rates, are investigated. In these models (i.e. reaction-diffusion and drop-push systems), we have the case of distinct particles where each particle $A_{\alpha }$ has its own intrinsic hopping rate $v_{\alpha }$. They also contain the parameters that control the annihilation-diffusion rates (including pair-annihilation and coagulation to the right and left). We obtain two distinct new models. It is shown that these models are exactly solvable in the sense of the Bethe anstaz. The two-particle conditional probabilities and the large-time behavior of such systems are also calculated.

arXiv comment17 pages, without figure

References in corpus (18)

• Nonequilibrium Statistical Mechanics of the Zero-Range Process and Related Models
• Particle hopping models and traffic flow theory
• Exact Solution of the Master Equation for the Asymmetric Exclusion Process
• Condensation in the zero range process: stationary and dynamical properties
• Current fluctuations in the zero-range process with open boundaries
• Zero-range process with open boundaries
• Dynamics of the condensate in zero-range processes
• Zero range model of traffic flow
• A two--parametric family of asymmetric exclusion processes and its exact solution
• Exact solution of a one-parameter family of asymmetric exclusion processes
• The Asymmetric Avalanche Process
• A new class of integrable diffusion-reaction processes
• On the solvable multi-species reaction-diffusion processes
• Annihilation-diffusion processes: an exactly solvable model
• Solvable multi-species extensions of the drop-push model
• A Remark on Integrability of Stochastic Systems Solvable by Matrix Product Ansatz
• Multi-species extension of the solvable partially asymmetric reaction- diffusion processes
• Solvable multi-species reaction-diffusion processes, including the extended drop-push model