arXiv subjects

Farhad H. Jafarpour

Publications and source records attributed to Farhad H. Jafarpour.

23 records · Page 2Linked to original sources

arXiv2008

Connection between matrix-product states and superposition of Bernoulli shock measures

We consider a generalized coagulation-decoagulation system on a one-dimensional discrete lattice with reflecting boundaries. It is known that a Bernoulli shock measure with two shock fronts might have a simple random-walk dynamics, provided that some constraints on the microscopic reaction rates of this system are fulfilled. Under these constraints the steady-state of the system can be written as a linear superposition of such shock measures. We show that the coefficients of this expansion can be calculated using the finite-dimensional representation of the quadratic algebra of the system obtained from a matrix-product approach.

cond-mat.stat-mech↗

arXiv2008

Finite-dimensional representation of the quadratic algebra of a generalized coagulation-decoagulation model

The steady-state of a generalized coagulation-decoagulation model on a one-dimensional lattice with reflecting boundaries is studied using a matrix-product approach. It is shown that the quadratic algebra of the model has a four-dimensional representation provided that some constraints on the microscopic reaction rates are fulfilled. The dynamics of a product shock measure with two shock fronts, generated by the Hamiltonian of this model, is also studied. It turns out that the shock fronts move on the lattice as two simple random walkers which repel each other provided that the same constraints on the microscopic reaction rates are satisfied.

cond-mat.stat-mech↗

arXiv2005

Multiple Shocks in a Driven Diffusive System with Two Species of Particles

A one-dimensional driven diffusive system with two types of particles and nearest neighbors interactions has been considered on a finite lattice with open boundaries. The particles can enter and leave the system from both ends of the lattice and there is also a probability for converting the particle type at the boundaries. We will show that on a special manifold in the parameters space multiple shocks evolve in the system for both species of particles which perform continuous time random walks on the lattice.

cond-mat.stat-mech↗

arXiv2004

Numerical Study of Phase Transition in an Exclusion Model with Parallel Dynamics

A numerical method based on Matrix Product Formalism is proposed to study the phase transitions and shock formation in the Asymmetric Simple Exclusion Process with open boundaries and parallel dynamics. By working in a canonical ensemble, where the total number of the particles is being fixed, we find that the model has a rather non-trivial phase diagram consisting of three different phases which are separated by second-order phase transition. Shocks may evolve in the system for special values of the reaction parameters.

cond-mat.stat-mech↗

arXiv2004

Shock in a Branching-Coalescing Model with Reflecting Boundaries

A one-dimensional branching-coalescing model is considered on a chain of length L with reflecting boundaries. We study the phase transitions of this model in a canonical ensemble by using the Yang-Lee description of the non-equilibrium phase transitions. Numerical study of the canonical partition function zeros reveals two second-order phase transitions in the system. Both transition points are determined by the density of the particles on the chain. In some regions the density profile of the particles has a shock structure.

cond-mat.stat-mech↗