Statistical mechanics derivation of hydrodynamic boundary conditions: the diffusion equation

Details Statistical mechanics derivation of hydrodynamic boundary conditions: the diffusion equation Statistical mechanics derivation of hydrodynamic boundary conditions: the diffusion equation

2002-05-13

arxiv.org/abs/cond-mat/0205255v2

Physics

Condensed Matter

Statistical Mechanics

15 pages; slightly revised and shortened version; J. Phys.: Condens. Matter in print

Scientific paper

10.1088/0953-8984/14/40/313

Considering the example of interacting Brownian particles we present a linear response derivation of the boundary condition for the corresponding hydrodynamic description (the diffusion equation). This requires us to identify a non-analytic structure in a microscopic relaxation kernel connected to the frequency dependent penetration length familiar for diffusive processes, and leads to a microscopic definition of the position where the hydrodynamic boundary condition has to be applied. Corrections to the hydrodynamic limit are obtained and we derive general amplitudes of spatially and temporally long ranged states in the considered diffusive system.

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