05-193 R. van Zon, E. G. D. Cohen
Theorem on the Distribution of Short-Time Single Particle Displacements with Physical Applications (97K, Latex 2e + 1 figure) May 30, 05
Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

Abstract. The distribution of the initial short-time displacements of a single particle is considered for a class of classical systems of particles under rather general conditions. This class of systems contains canonical equilibrium of a multi-component Hamiltonian system as a special case. We prove that for this class of systems the nth order cumulant of the initial short-time displacements behaves as the 2n-th power of time for all n>2, rather than exhibiting a general nth power scaling. This has direct applications to the initial short-time behavior of the Van Hove self-correlation function, to its non-equilibrium generalizations the Green's functions for mass transport, and to the non-Gaussian parameters used in supercooled liquids and glasses. Moreover, in the context of the Green's functions this theorem is expected to be relevant for mass transport at (sub)picosecond time scales.

Files: 05-193.src( 05-193.comments , 05-193.keywords , paper.tex , figure1.eps )