An exact solution of a one-dimensional asymmetric exclusion model with open boundaries

@article{Derrida1992AnES,
  title={An exact solution of a one-dimensional asymmetric exclusion model with open boundaries},
  author={Bernard Derrida and Eytan Domany and David Mukamel},
  journal={Journal of Statistical Physics},
  year={1992},
  volume={69},
  pages={667-687}
}
A simple asymmetric exclusion model with open boundaries is solved exactly in one dimension. The exact solution is obtained by deriving a recursion relation for the steady state: if the steady state is known for all system sizes less thanN, then our equation (8) gives the steady state for sizeN. Using this recursion, we obtain closed expressions (48) for the average occupations of all sites. The results are compared to the predictions of a mean field theory. In particular, for infinitely large… 

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References

SHOWING 1-10 OF 20 REFERENCES

Diffusion in concentrated lattice gases. III. Tracer diffusion on a one-dimensional lattice

The dynamical process of the diffusion of tagged particles in a one-dimensional concentrated lattice gas is investigated. The particles are noninteracting except that double occupancy is forbidden.

A remark on the hydrodynamics of the zero-range processes

The nonequilibrium stationary hydrodynamical properties of the symmetric nearest neighbor zero-range processes are studied: local equilibrium and Fourier's law are proven to hold, and the bulk

Exclusion process and droplet shape

We use a mathematical isomorphism between the one-dimensional exclusion process and the two-dimensional stochastic Ising model in the low-temperature limit to describe the typical instantaneous shape

Wetting dynamics: two simple models

Two models of the wetting dynamics of a non-volatile liquid are introduced. Both models exhibit a transition between partial and complete wetting regimes. The first model, which can also be viewed as

Rigorous derivation of domain growth kinetics without conservation laws

The time evolution of the Ising model that describes shrinking domains is studied. A singly connected domain of Ising spins, embedded in a sea of the opposite phase, develops atT=0 according to a

Nonequilibrium measures which exhibit a temperature gradient: Study of a model

We give some rules to define measures which could describe heat flow in homogeneous crystals. We then study a particular model which is explicitly solvable: the one dimensional nearest neighborhood

Non-equilibrium behaviour of a many particle process: Density profile and local equilibria

SummaryOne considers a simple exclusion particle jump process on ℤ, where the underlying one particle motion is a degenerate random walk that moves only to the right. One starts with the

Excess noise for driven diffusive systems.

TLDR
The steady-state scattering function for driven diffusive systems with a single conserved density is investigated and it is found that d = 2 is the borderline dimension with marginally nondiffusive behavior; for d larger than 2 the spread is diffusive with anisotropic long-time-tail corrections.

Fluctuations of a stationary nonequilibrium interface.

We study properties of interfaces between stationary phases of the two-dimensional discrete-time Toom model (north-east-center majority vote with small noise): phases not described by equilibrium

Dynamic scaling of growing interfaces.

TLDR
A model is proposed for the evolution of the profile of a growing interface that exhibits nontrivial relaxation patterns, and the exact dynamic scaling form obtained for a one-dimensional interface is in excellent agreement with previous numerical simulations.