 05193 R. van Zon, E. G. D. Cohen
 Theorem on the Distribution of ShortTime Single Particle Displacements with Physical Applications
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May 30, 05

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Abstract. The distribution of the initial shorttime 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 multicomponent Hamiltonian system as a
special case. We prove that for this class of systems the nth order
cumulant of the initial shorttime displacements behaves as the
2nth power of time for all n>2, rather than exhibiting a general
nth power scaling. This has direct applications to the initial
shorttime behavior of the Van Hove selfcorrelation function, to its
nonequilibrium generalizations the Green's functions for mass
transport, and to the nonGaussian 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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