Constraints on collective density variables: One dimension

Collective density variables ρ(k) are frequently employed in many-body physics to describe a wide variety of static and dynamic phenomena. These variables are nonlinear functions of particle positions, and consequently exhibit subtle couplings and kinematic constraints. We examine some of these features for one-dimensional systems, using both numerical exploration and analytical techniques. In particular we have considered the consequences of quenching density fluctuations [minimizing the ρ(k)’s] for sets of wave vectors surrounding the origin. This is shown, under proper circumstances, to force other sets of ρ(k)’s automatically to their minima, and even to induce perfect crystallization of the many-particle system.