×

Fluctuations in the weakly asymmetric exclusion process with open boundary conditions. (English) Zbl 1073.82029

The authors study the fluctuations of the stationary distribution of the one-dimensional weakly asymmetric exclusion process with two open boundaries, which physically describes the stochastic evolution of particle distribution on one-dimensional lattice of \(L\) sites under weakly-directed external field [cf. B. Derrida, C. Enaud, and J. L. Lebowitz J. Stat. Phys. 115, No. 1–2, 365–382 (2004)]. By both dynamic and static approaches, it is shown that in the limit of \(L\to\infty\) these fluctuations are given by a centered Gaussian field with its covariance function explicitly calculated. The dynamic approach is based on searching for the stationary solutions of the evolution equation of the fluctuations. The static one is based on a representation of the steady state as a sum over two paths related to Brownian motion and potential respectly. The results show that the weakly asymmetric case differs from the totally asymmetric case as well as the symmetric case.

MSC:

82C22 Interacting particle systems in time-dependent statistical mechanics
60K35 Interacting random processes; statistical mechanics type models; percolation theory
82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics
82C05 Classical dynamic and nonequilibrium statistical mechanics (general)
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[5] A. de Masi, N. Ianiro, A. Pellegrinotti, and E. Presutti, A survey of the hydrodynamical behavior of many-particle systems in Non Equilibrium Phenomena II: From Stochastics to Hydrodynamics, J. L. Lebowitz and E. W. Montroll (North-Holland physics publishing, Amsterdam 1984). · Zbl 0567.76006
[12] C. Landim, A. Milanes, and S. Olla, Fluctuations of the weakly asymmetric exclusion process in contact with reservoirs, in preparation.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.