Collective Coordinate Control of Density Distributions

Obioma Uche, Princeton University

Real collective density variables C(k) in many-particle systems arise from non-linear transformations of particle positions, and can determine the structure factor S(k). Here, we examine features associated with collective density variables in one, two, and three dimensions using numerical exploration techniques to generate particle patterns in the classical ground state. In addition, we demonstrate the capacity to control S(k) in the neighborhood of |k| = 0. The optimization method employed generates multi-particle configurations for which S(k) ∝ |k|^α, |k| ≤ K, and α = 1, 2, 4, 6, 8, and 10. The case α = 1 is relevant for the Harrison-Zeldovich model of the early universe, for superfluid 4He, and for jammed amorphous sphere packings. The analysis also provides specific examples of interaction potentials whose classical ground state are configurationally degenerate.


References:

1) Y. Fan, J. K. Percus, D. K. Stillinger and F. H. Stillinger, Constraints on Collective Density Variables: One Dimension, Physical Review A 44, 2394-2402 (1991).

2) O. U. Uche, F. H. Stillinger, and S. Torquato, Constraints on Collective Density Variables: Two Dimensions, Physical Review E, 70, 046112 (2004).

3) O. U. Uche, F. H. Stillinger, and S. Torquato, Collective Coordinate Control of Density Distributions, submitted to Physical Review E.

Abstract Author(s): O. U. Uche, F. H. Stillinger, and S. Torquato