Theorem on the Distribution of Short Time Single Particle Displacements

Details Theorem on the Distribution of Short Time Single Particle Displacements Theorem on the Distribution of Short Time Single Particle Displacements

2005-09-30

arxiv.org/abs/cond-mat/0510004v1

Physica A 365, 108-112 (2006)

Physics

Condensed Matter

Statistical Mechanics

Short 8 page pedagogical review of cond-mat/0505734 for Proc. of "News, Expectations and Trends in Statistical Physics", Crete

Scientific paper

10.1016/j.physa.2006.01.035

The distribution of the initial very short-time displacements of a single particle is considered for a class of classical systems with Gaussian initial velocity distributions and arbitrary initial particle positions. A very brief sketch is given of a rather intricate and lengthy proof that for this class of systems the nth order cumulants behave as t^{2n} for all n>2, rather than as t^{n}. We also briefly discuss some physical consequences for liquids.

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