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Strong asymmetric limit of the quasi-potential of the boundary driven weakly asymmetric exclusion process | | Lorenzo Bertini
; Davide Gabrielli
; Claudio Landim
; | | Date: |
13 Jun 2008 | | Abstract: | We consider the weakly asymmetric exclusion process on a bounded interval
with particles reservoirs at the endpoints. The hydrodynamic limit for the
empirical density, obtained in the diffusive scaling, is given by the viscous
Burgers equation with Dirichlet boundary conditions. In the case in which the
bulk asymmetry is in the same direction as the drift due to the boundary
reservoirs, we prove that the quasi-potential can be expressed in terms of the
solution to a one-dimensional boundary value problem which has been introduced
by Enaud and Derrida cite{de}. We consider the strong asymmetric limit of the
quasi-potential and recover the functional derived by Derrida, Lebowitz, and
Speer cite{DLS3} for the asymmetric exclusion process. | | Source: | arXiv, 0806.2296 | | Services: | Forum | Review | PDF | Favorites | |
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