A limit result for a system of particles in random environment

We consider an infinite system of particles in one dimension, each particle performs independant Sinai's random walk in random environment. Considering an instant $t$, large enough, we prove a result in probability showing that the particles are trapped in the neighborhood of well defined points of the lattice depending on the random environment the time $t$ and the starting point of the particles.Comment: 11 page

A new class of integrable diffusion-reaction processes

We consider a process in which there are two types of particles, A and B, on an infinite one-dimensional lattice. The particles hop to their adjacent sites, like the totally asymmetric exclusion process (ASEP), and have also the following interactions: A+B -> B+B and B+A -> B+B, all occur with equal rate. We study this process by imposing four boundary conditions on ASEP master equation. It is shown that this model is integrable, in the sense that its N-particle S-matrix is factorized into a product of two-particle S-matrices and, more importantly, the two-particle S-matrix satisfy quantum Yang-Baxter equation. Using coordinate Bethe-ansatz, the N-particle wavefunctions and the two-particle conditional probabilities are found exactly. Further, by imposing four reasonable physical conditions on two-species diffusion-reaction processes (where the most important ones are the equality of the reaction rates and the conservation of the number of particles in each reaction), we show that among the 4096 types of the interactions which have these properties and can be modeled by a master equation and an appropriate set of boundary conditions, there are only 28 independent interactions which are integrable. We find all these interactions and also their corresponding wave functions. Some of these may be new solutions of quantum Yang-Baxter equation.Comment: LaTex,16 pages, some typos are corrected, will be appeared in Phys. Rev. E (2000

Motion of a driven tracer particle in a one-dimensional symmetric lattice gas

We study the dynamics of a tracer particle subject to a constant driving force $E$ in a one-dimensional lattice gas of hard-core particles whose transition rates are symmetric. We show that the mean displacement of the driven tracer grows in time, $t$, as $\sqrt{\alpha t}$, rather than the linear time dependence found for driven diffusion in the bath of non-interacting (ghost) particles. The prefactor $\alpha$ is determined implicitly, as the solution of a transcendental equation, for an arbitrary magnitude of the driving force and an arbitrary concentration of the lattice gas particles. In limiting cases the prefactor is obtained explicitly. Analytical predictions are seen to be in a good agreement with the results of numerical simulations.Comment: 21 pages, LaTeX, 4 Postscript fugures, to be published in Phys. Rev. E, (01Sep, 1996

Disorder effect on the traffic flow behavior

45.70.Vn Granular models of complex systems; traffic flow, 45.50.-j ynamics and kinematics of a particle and a system of particles, 45.70.Mg Granular flow: mixing, segregation and stratification, 47.57.Gc Granular flow,