Collective diffusion of lattice gases on linear chains with site-energy disorder

Kehr, K. W.; Paetzold, O. H.; Wichmann, Thomas

doi:10.1016/0375-9601(93)90067-a

Cited by 12 publications

(8 citation statements)

References 14 publications

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“…From the physical point of view, diffusion of lattice gases in systems with site disorder has been studied mainly by means of simulations and more or less rough approximations like mean field . We refer the interested reader to [19], [20], [21], [22], [24] and to [17] for an iterative procedure to compute corrections to the mean-field approximation.…”

Section: Introductionmentioning

confidence: 99%

Hydrodynamic limit of a disordered lattice gas

Faggionato

Martinelli

2003

Probab. Theory Relat. Fields

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ABSTRACT. We consider a model of lattice gas dynamics in Z d in the presence of disorder. If the particle interaction is only mutual exclusion and if the disorder field is given by i.i.d. bounded random variables, we prove the almost sure existence of the hydrodynamical limit in dimension d ≥ 3. The limit equation is a non linear diffusion equation with diffusion matrix characterized by a variational principle. MSC: 60K40, 60K35, 60J27, 82B10, 82B20

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Section: Introductionmentioning

confidence: 99%

Hydrodynamic limit of a disordered lattice gas

Faggionato

Martinelli

2003

Probab. Theory Relat. Fields

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“…systems involving randomly moving particles with hard-core interactions, have received much interest within the last several decades. A number of important theoretical results have been obtained for such systems revealing non-trivial, many-body behavior [1][2][3][4][5][6][7][8][9][10][11][12]. Lattice gas models often serve as microscopic models of complex physical phenomena.…”

Section: Introductionmentioning

confidence: 99%

Motion of a driven tracer particle in a one-dimensional symmetric lattice gas

et al. 1996

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“…Such systems have been used to model electron transport in doped crystals [1,2,3,8,10,12,14]. In this case, the hard core exclusion rule is given by the Pauli exclusion principle.…”

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confidence: 99%

Bulk diffusion in a system with site disorder

Quastel¹

2006

Ann. Probab.

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We consider a system of random walks in a random environment interacting via exclusion. The model is reversible with respect to a family of disordered Bernoulli measures. Assuming some weak mixing conditions, it is shown that, under diffusive scaling, the system has a deterministic hydrodynamic limit which holds for almost every realization of the environment. The limit is a nonlinear diffusion equation with diffusion coefficient given by a variational formula. The model is nongradient and the method used is the ``long jump'' variation of the standard nongradient method, which is a type of renormalization. The proof is valid in all dimensions.Comment: Published at http://dx.doi.org/10.1214/009117906000000322 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

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Collective diffusion of lattice gases on linear chains with site-energy disorder

Cited by 12 publications

References 14 publications

Hydrodynamic limit of a disordered lattice gas

Hydrodynamic limit of a disordered lattice gas

Motion of a driven tracer particle in a one-dimensional symmetric lattice gas

Bulk diffusion in a system with site disorder

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