Related papers: Matrix product solution to multi-species ASEP with…
The traffic of molecular motors through open tube-like compartments is studied using lattice models. These models exhibit boundary-induced phase transitions related to those of the asymmetric simple exclusion process (ASEP) in one…
We propose a model for cell polarization as a response to an external signal which results in a system of PDEs for different variants of a protein on the cell surface and interior respectively. We study stationary states of this model in…
We introduce a general method to determine the large scale non-equilibrium steady-state properties of one-dimensional multi-species driven diffusive systems with open boundaries, generalizing thus the max-min current principle known for…
Research in combinatorics has often explored the asymmetric simple exclusion process (ASEP). The ASEP, inspired by examples from statistical mechanics, involves particles of various species moving around a lattice. With the traditional ASEP…
We present a general construction of matrix product states for stationary density matrices of one-dimensional quantum spin systems kept out of equilibrium through boundary Lindblad dynamics. As an application we review the isotropic…
We study the nonequilibrium steady states in totally asymmetric exclusion processes (TASEP) with open boundary conditions having spatially inhomogeneous hopping rates. Considering smoothly varying hopping rates, we show that the steady…
We present a complete set of analytical and invariant expressions for the steady-state density matrix of atoms in a resonant radiation field with arbitrary intensity and polarization. The field drives the closed dipole transition with…
We explore how the interplay of finite availability, carrying capacity of particles at different parts of a spatially extended system and particle diffusion between them control the steady state currents and density profiles in a…
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…
We derive the Bethe ansatz equations describing the complete spectrum of the transition matrix of the partially asymmetric exclusion process with the most general open boundary conditions. For totally asymmetric diffusion we calculate the…
Using a matrix product method the steady-state of a family of disordered reaction-diffusion systems consisting of different species of interacting classical particles moving on a lattice with periodic boundary conditions is studied. A new…
Theoretical advances in the study of non-equilibrium phenomena are briefly reviewed with emphasis on steady state properties of one-dimensional driven lattice gases. The presentation is focused on the totally asymmetric simple-exclusion…
The one-dimensional partially asymmetric simple exclusion process with open boundaries is considered. The stationary state, which is known to be constructed in a matrix product form, is studied by applying the theory of q-orthogonal…
We show that the known matrix representations of the stationary state algebra of the Asymmetric Simple Exclusion Process (ASEP) can be interpreted combinatorially as various weighted lattice paths. This interpretation enables us to use the…
We explore the stationary densities in totally asymmetric exclusion processes (TASEP) with open boundary conditions and spatially inhomogeneous hopping rates. We calculate the steady state density profiles that characterise the associated…
We show in the example of a one-dimensional asymmetric exclusion process that stationary states of models with parallel dynamics may be written in a matrix product form. The corresponding algebra is quadratic and involves three different…
We introduce a mean-field theoretical framework to describe multiple totally asymmetric simple exclusion processes (TASEPs) with different lattice lengths, entry and exit rates, competing for a finite reservoir of particles. We present…
We consider a multi-species generalization of the Asymmetric Simple Exclusion Process on an open chain, in which particles hop with their characteristic hopping rates and fast particles can overtake slow ones. The number of species is…
We find the formulas of the transition probabilities of the $N$-particle multi-species asymmetric simple exclusion processes (ASEP), and show that the transition probabilities are written as a determinant when the order of particles in the…
We study the one dimensional partially asymmetric simple exclusion process (ASEP) with open boundaries, that describes a system of hard-core particles hopping stochastically on a chain coupled to reservoirs at both ends. Derrida, Evans,…