An Investigation of the Realizability of Correlation Functions

Obioma Uche, Princeton University

The pair correlation function g_2(r) describes short-range order in many-particle systems, It must obey two necessary conditions: (i) non-negativity for all distances r, and (ii) non-negativity of its associated structure factor S(k) for all k. In inverse reconstruction, knowledge of a given target function can be used to evolve a random arrangement of hard particles towards a state in which its final configuration yields a good approximation to the target function. The series of evolving configurations are induced by application of a simulated annealing algorithm. We aim to explore the inverse construction problem for densities up to and beyond the terminal density for a variety of target functions. In our present study, our target functions are the unit step and the delta-unit step radial distribution functions. Our results indicate that the former target function is realizable up to a terminal density at which the packing fraction of particle exclusion diameters equals 2-d in d dimensions. In addition, the delta-unit step function is achievable up to a terminal density of (d+2)/(2d+1) in d dimensions for a system of hard particles.

Abstract Author(s): Obioma U. Uche, Frank H. Stillinger, and Salvatore Torquato