Related papers: Bethe Ansatz for the Weakly Asymmetric Simple Excl…
We study the fluctuations of the total current for the partially asymmetric exclusion process in the scaling of a weak asymmetry (asymmetry of order the inverse of the size of the system) using Bethe Ansatz. Starting from the functional…
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 use the Bethe Ansatz to derive analytical expressions for the current statistics in the asymmetric exclusion process with both forward and backward jumps. The Bethe equations are highly coupled and this fact has impeded their use to…
Using the Bethe ansatz we obtain in a determinant form the exact solution of the master equation for the conditional probabilities of the totally asymmetric exclusion process with particle-dependent hopping rates on Z. From this we derive a…
We conjecture an exact expression for the large deviation function of the stationary state current in the partially asymmetric exclusion process with periodic boundary conditions. This expression is checked for small systems using…
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…
By an extension of the Bethe ansatz method used by Gwa and Spohn, we obtain an exact expression for the large deviation function of the time averaged current for the fully asymmetric exclusion process in a ring containing $N$ sites and $p$…
The fluctuations of the current for the one-dimensional totally asymmetric exclusion process with $L$ sites are studied in the relaxation regime of times $T\sim L^{3/2}$. Using Bethe ansatz for the periodic system with an evolution…
We consider the asymmetric simple exclusion process in one dimension with weak asymmetry (WASEP) and 0-1 step initial condition. Our interest are the fluctuations of the time-integrated particle current at some prescribed spatial location.…
This paper presents the exact expressions of the transition probabilities of some non-determinantal Bethe ansatz solvable interacting particle systems: the two-sided PushASEP, the asymmetric avalanche process and the asymmetric zero range…
We use functional Bethe Ansatz equations to calculate the cumulants of the total current in the partially asymmetric exclusion process. We recover known formulas for the first two cumulants (mean value of the current and diffusion constant)…
The relaxation dynamics of the one-dimensional totally asymmetric simple exclusion process on a ring is considered in the case of step initial condition. Analyzing the time evolution of the local particle densities and currents by the Bethe…
We study current fluctuations of a two-species asymmetric exclusion process, known as the Arndt-Heinzel-Rittenberg model. For a step-Bernoulli initial condition with finite number of particles, we provide an explicit multiple integral…
We consider the facilitated exclusion process, an interacting particle system on the integer line where particles hop to one of their left or right neighbouring site only when the other neighbouring site is occupied by a particle. A…
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…
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 consider the weakly asymmetric simple exclusion process on a ring, driven out of equilibrium by tilting the dynamics so as to enforce a macroscopic current of particles on a large time interval. In this current-biased dynamics, the tilt…
We analyze the Bethe ansatz equations describing the complete spectrum of the transition matrix of the partially asymmetric exclusion process on a finite lattice and with the most general open boundary conditions. We extend results obtained…
We study the weakly asymmetric simple exclusion process in one dimension. We prove sample path moderate deviation principles for the current and the tagged particle when the process starts from one of its stationary measures. We simplify…
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…