Diffusive Limit of the Asymmetric Simple Exclusion: The Navier-Stokes Correction

摘要: We consider the simple exclusion process (SEP) on a cubic sublattice, Λ L ⊂ Z d , of size 2L + 1, with periodic boundary conditions. The dynamics is as follows. Let e denote one 2d possible directions in . A particle site x, independently others, waits for an exponential time and jumps, probability proportional to p ≥ 0, x e, if it empty; otherwise stays starts again. by η (τ) = 0,1 number particles at τ generator process: f ∑b b f, sum running set all oriented bonds (x,y) such that y − $$ {{L}_{b}}f {{p}_{e}}{{\eta }_{x}}\left[ {f\left( {{{\eta }^{b}}} \right) - f\left( \eta \right)} \right] $$ (1) with ({{n}^{b}})z ({{n}^{{x,y}}})z \left\{ {\begin{array}{*{20}{c}} }_{y}},} & {if} {z x} \\ }_{x}},} y} }_{z}},} {otherwise.} \end{array} } \right. $$ It convenient choose normalization −e 2 e.