Shocks in the asymmetric exclusion process

Schütz

et al. 1998

J. Phys. A: Math. Gen.

370

501

Abstract. We consider the asymmetric simple exclusion process (ASEP) with open boundaries and other driven stochastic lattice gases of particles entering, hopping and leaving a onedimensional lattice. The long-term system dynamics, stationary states, and the nature of phase transitions between steady states can be understood in terms of the interplay of two characteristic velocities, the collective velocity and the shock (domain wall) velocity. This interplay results in two distinct types of domain walls whose dynamics is computed. We conclude that the phase diagram of the ASEP is generic for one-component driven lattice gases with a single maximum in the current-density relation.

Section: Introductionmentioning

confidence: 99%

Phase diagram of one-dimensional driven lattice gases with open boundaries

Schütz

et al. 1998

J. Phys. A: Math. Gen.

370

501

“…Therefore it moves forward in an environment of low density of particles and backwards in a high density environment. In this way a second class particle can be used to locate shocks which are sudden changes in density over a microscopic region [11,12,13,14]. A generalisation of the second class particle idea to that of a defect particle [15,16] has been shown to exhibit phase transitions and, in particular, phase coexistence.…”

Section: Introduction and Model Definitionmentioning

confidence: 99%

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

Derrida

Evans

1999

J. Phys. A: Math. Gen.

128

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 limit behaviour of the generating function of the distance travelled by the defect particle. This allows us to recover steady state properties known from the matrix approach such as the velocity, and obtain new results such as the diffusion constant of the defect particle. In the case where the defect particle is a second class particle we determine the large deviation function and show that in a certain range the distribution of the distance travelled about the mean is Gaussian. Moreover the variance (diffusion constant) grows as L 1/2 where L is the system size. This behaviour can be related to the superdiffusive spreading of excess mass fluctuations on an infinite system. In the case where the defect particle produces a shock, our expressions for the velocity and the diffusion constant coincide with those calculated previously for an infinite system by Ferrari and Fontes.

“…[6] and [4]. Since SCPs are in general attracted by shocks which often appear in one-dimensional driven diffusive systems, SCPs can also be used to obtain a good definition of the microscopic position of shocks [1,2], [7]- [11].…”

Section: Introductionmentioning

confidence: 99%

Estimation of Surface Tension of Molten Silicon Using a Dynamic Hanging Drop

Chung¹,

Izunome²,

Yokotani³

et al. 1995

Jpn. J. Appl. Phys.

We consider the one-dimensional Katz-Lebowitz-Spohn (KLS) model, which is a generalization of the totally asymmetric simple exclusion process (TASEP) with nearest neighbour interaction. Using a powerful mapping, the KLS model can be translated into a misanthrope process. In this model, for the repulsive case, it is possible to introduce second-class particles, the number of which is conserved. We study the distance distribution of second-class particles in this model numerically and find that for large distances it decreases as x −3/2 . This agrees with a previous analytical result of for the TASEP, where the same asymptotic behaviour was found. We also study the dynamical scaling function of the distance distribution and find that it is universal within this family of models.