Exact and asymtotic formulas for overdamped Brownian dynamics

Details Exact and asymtotic formulas for overdamped Brownian dynamics Exact and asymtotic formulas for overdamped Brownian dynamics

1996-10-10

arxiv.org/abs/cond-mat/9610085v1

Physica A 238 (1997) 405

Physics

Condensed Matter

Statistical Mechanics

18 pages,LaTex

Scientific paper

Exact and asymptotic formulas relating to dynamical correlations for overdamped Brownian motion are obtained. These formulas include a generalization of the $f$-sum rule from the theory of quantum fluids, a formula relating the static current-current correlation to the static density-density correlation, and an asymptotic formula for the small-$k$ behaviour of the dynamical structure factor. Known exact evaluations of the dynamical density-density correlation in some special models are used to illustrate and test the formulas.

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