Related papers: Exact solution of a one-parameter family of asymme…
A two-parameter family of discrete-time exactly-solvable exclusion processes on a one-dimensional lattice is introduced, which contains the asymmetric simple exclusion process and the drop-push model as particular cases. The process is…
A two--parameter family of asymmetric exclusion processes for particles on a one-dimensional lattice is defined. The two parameters of the model control the driving force and an effect which we call pushing, due to the fact that particles…
Using the Bethe ansatz, we obtain the exact solution of the master equation for the totally asymmetric exclusion process on an infinite one-dimensional lattice. We derive explicit expressions for the conditional probabilities P(x_1, ...…
The exact solution of the asymmetric exclusion problem with particles of first and second class is presented. In this model the particles (size 1) of both classes are attached on lattice points and diffuse with equal asymmetric rates, but…
We consider the totally asymmetric exclusion process in discrete time with generalized updating rules. We introduce a control parameter into the interaction between particles. Two particular values of the parameter correspond to known…
The exact solution of the asymmetric exclusion problem with N distinct classes of particles (c = 1,2,...,N), with hierarchical order is presented. In this model the particles (size 1) are located at lattice points, and diffuse with equal…
The asymmetric exclusion process on a ring in one-dimension is considered with a single defect particle. The steady state has previously been solved by a matrix product method. Here we use the Bethe ansatz to solve exactly for the long time…
A family of boundary conditions corresponding to exclusion processes is introduced. This family is a generalization of the boundary conditions corresponding to the simple exclusion process, the drop-push model, and the one-parameter…
We consider the totally asymmetric exclusion process in discrete time with the parallel update. Constructing an appropriate transformation of the evolution operator, we reduce the problem to that solvable by the Bethe ansatz. The…
The one-dimensional asymmetric simple exclusion process (ASEP), where $N$ hard-core particles hop forward with rate $1$ and backward with rate $q<1$, is considered on a periodic lattice of $L$ site. Using KPZ universality and previous…
The exact solution of the asymmetric exclusion problem and several of its generalizations is obtained by a matrix product {\it ansatz}. Due to the similarity of the master equation and the Schr\"odinger equation at imaginary times the…
In this thesis, we consider one of the most popular models of non-equilibrium statistical physics: the Asymmetric Simple Exclusion Process, in which particles jump stochastically on a one-dimensional lattice, between two reservoirs at fixed…
We consider an exclusion process on a periodic one-dimensional lattice where all particles perform simple symmetric exclusion at rate $1$ except for a single tracer particle, which performs partially simple asymmetric exclusion with rate…
By considering the master equation of asymmetric exclusion process on a one-dimensional lattice, we obtain the most general boundary condition of the multi-species exclusion processes in which the number of particles is constant in time.…
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,…
The totally asymmetric simple exclusion process (TASEP) is a stochastic model for the unidirectional flow of interacting particles on a 1D-lattice that is much used in systems biology and statistical physics. Its master equation describes…
A discrete-time totally asymmetric simple exclusion process on a lattice with open boundaries is considered. There are particles of different types. The type of a particle is characterized by the probability that a particle moves to a…
We study the transition probabilities for the totally asymmetric simple exclusion process (TASEP) on the infinite integer lattice with a finite, but arbitrary number of first and second class particles. Using the Bethe ansatz we present an…
The totally asymmetric simple exclusion process (TASEP) is a stochastic model for the unidirectional dynamics of interacting particles on a $1$D-lattice that is much used in systems biology and statistical physics. Its master equation…
A generalization of the simple exclusion asymmetric model is introduced. In this model an arbitrary mixture of molecules with distinct sizes $s = 0,1,2,...$, in units of lattice space, diffuses asymmetrically on the lattice. A related…