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

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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.

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