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)

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.