Related papers: Family of Commuting Operators for the Totally Asym…
We fully elucidate the structure of the hierarchy of the connected operators that commute with the Markov matrix of the Totally Asymmetric Exclusion Process (TASEP). We prove for the connected operators a combinatorial formula that was…
We derive, using the algebraic Bethe Ansatz, a generalized Matrix Product Ansatz for the asymmetric exclusion process (ASEP) on a one-dimensional periodic lattice. In this Matrix Product Ansatz, the components of the eigenvectors of the…
In this paper, we look at the asymmetric simple exclusion process with open boundaries with a current-counting deformation. We construct a two-parameter family of transfer matrices which commute with the deformed Markov matrix of the…
The asymmetric simple exclusion process (ASEP) is a paradigm for non-equilibrium physics that appears as a building block to model various low-dimensional transport phenomena, ranging from intracellular traffic to quantum dots. We review…
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…
We study the spectrum of the Markov matrix of the totally asymmetric exclusion process (TASEP) on a one-dimensional periodic lattice at ARBITRARY filling. Although the system does not possess obvious symmetries except translation…
We study the one-dimensional totally asymmetric simple exclusion process in contact with two reservoirs including also a fugacity at one boundary. The eigenvectors and the eigenvalues of the corresponding Markov matrix are computed using…
Using the Bethe ansatz we obtain the determinant expression for the time dependent transition probabilities in the totally asymmetric exclusion process with parallel update on a ring. Developing a method of summation over the roots of Bethe…
The asymmetric simple exclusion process (ASEP) plays the role of a paradigm in non-equilibrium statistical mechanics. We review exact results for the ASEP obtained by Bethe ansatz and put emphasis on the algebraic properties of this model.…
We implement the Bethe anstaz method for the elliptic quantum group $E_{\tau,\eta}(A_2^{(2)})$. The Bethe creation operators are constructed as polynomials of the Lax matrix elements expressed through a recurrence relation. We also give the…
To each representation of the elliptic quantum group $E_{\tau,\eta}(sl_2)$ is associated a family of commuting transfer matrices. We give common eigenvectors by a version of the algebraic Bethe ansatz method. Special cases of this…
We define the elliptic quantum group $E_{\tau,\eta}(so_3)$ and the transfer matrix corresponding to its simplest highest weight representation. We use Bethe anstaz method to construct the creation operators as polynomials of the Lax matrix…
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 asymmetric simple exclusion process with open boundaries, which is a very simple model of out-of-equilibrium statistical physics, is known to be integrable. In particular, its spectrum can be described in terms of Bethe roots. The large…
We present in this paper a comprehensive introduction to the algebraic Bethe Ansatz, taking as examples the six-vertex model with periodic and non-periodic boundary conditions. We propose a diagrammatic representation of the commutation…
We present a new derivation of the spectral gap of the totally asymmetric exclusion process on a half-filled ring of size L by using the Bethe Ansatz. We show that, in the large L limit, the Bethe equations reduce to a simple transcendental…
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…
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 eigenfunctions and eigenvalues of the master-equation for zero range process with totally asymmetric dynamics on a ring are found exactly using the Bethe ansatz weighted with the stationary weights of particle configurations. The Bethe…
The partially asymmetric exclusion process (PASEP) is an important model from statistical mechanics which describes a system of interacting particles hopping left and right on a one-dimensional lattice of $n$ sites. It is partially…