# Exact diffusion constant for one-dimensional asymmetric exclusion models

@article{Derrida1993ExactDC, title={Exact diffusion constant for one-dimensional asymmetric exclusion models}, author={Bernard Derrida and Martin R Evans and David Mukamel}, journal={Journal of Physics A}, year={1993}, volume={26}, pages={4911-4918} }

The one-dimensional fully asymmetric exclusion model, which describes a system of particles hopping in a preferred direction with hard core interactions, is considered on a ring of size N. The steady state of this system is known (all configurations have equal weight), which allows for easy computation of the average velocity of a particle in the steady state. Here an exact expression for the diffusion constant of a particle is obtained for arbitrary number of particles and system size, by…

## 74 Citations

### The totally asymmetric exclusion process on a ring: Exact relaxation dynamics and associated model of clustering transition

- Mathematics
- 2006

### Bethe ansatz solution for a defect particle in the asymmetric exclusion process

- Mathematics
- 1999

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…

### Exact diffusion constant for the one-dimensional partially asymmetric exclusion model

- Mathematics, Physics
- 1997

We calculate exactly the diffusion constant associated with the fluctuations of the current for the partial asymmetric exclusion model on a ring with an arbitrary number of particles and holes. We…

### Exact diffusion constant of a one-dimensional asymmetric exclusion model with open boundaries

- Mathematics
- 1995

For the 1D fully asymmetric exclusion model with open boundary conditions, we calculate exactly the fluctuations of the current of particles. The method used is an extension of a matrix technique…

### Tagged particle correlations in the asymmetric simple exclusion process: finite-size effects.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2007

It is shown that an exactly solvable linearized model captures the essential qualitative features seen in the finite-size effects of the tagged particle correlations in the ASEP, and provides an exact coarse-grained description of two other microscopic models.

### Exact steady states of disordered hopping particle models with parallel and ordered sequential dynamics

- Physics
- 1997

A one-dimensional driven lattice gas with disorder in the particle hopping probabilities is considered. It has previously been shown that in the version of the model with random sequential updating,…

### Exact Steady State Properties of the One Dimensional Asymmetric Exclusion Model

- Physics
- 1994

The asymmetric exclusion model describes a system of particles hopping in a preferred direction with hard core repulsion. Here we review several exact results concerning the steady state of this…

### One-dimensional asymmetric exclusion model with open boundaries

- Physics, Mathematics
- 1996

One-dimensional asymmetric exclusion model, in which the probabilities of hopping to the left and right are in general different, is studied. The boundaries are open; a particle is added at the left…

### Shocks in the asymmetry exclusion model with an impurity

- Physics
- 1996

We consider the one-dimensional asymmetric exclusion process with an impurity. This model describes particles hopping in one direction with stochastic dynamics and a hard core exclusion condition.…

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