arXiv subjects

S R Masharian

Publications and source records attributed to S R Masharian.

3 recordsLinked to original sources

arXiv2007

Matrix Product Steady States as Superposition of Product Shock Measures in 1D Driven Systems

It is known that exact traveling wave solutions exist for families of (n+1)-states stochastic one-dimensional non-equilibrium lattice models with open boundaries provided that some constraints on the reaction rates are fulfilled. These solutions describe the diffusive motion of a product shock or a domain wall with the dynamics of a simple biased random walker. The steady state of these systems can be written in terms of linear superposition of such shocks or domain walls. These steady states can also be expressed in a matrix product form. We show that in this case the associated quadratic algebra of the system has always a two-dimensional representation with a generic structure. A couple of examples for n=1 and n=2 cases are presented.

cond-mat.stat-mech↗

arXiv2007

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

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.

cond-mat.stat-mech↗

arXiv2005

Exact Shock Profile for the ASEP with Sublattice-Parallel Update

We analytically study the one-dimensional Asymmetric Simple Exclusion Process (ASEP) with open boundaries under sublattice-parallel updating scheme. We investigate the stationary state properties of this model conditioned on finding a given particle number in the system. Recent numerical investigations have shown that the model possesses three different phases in this case. Using a matrix product method we calculate both exact canonical partition function and also density profiles of the particles in each phase. Application of the Yang-Lee theory reveals that the model undergoes two second-order phase transitions at critical points. These results confirm the correctness of our previous numerical studies.

cond-mat.stat-mech↗