Density fluctuations in many-body systems

Abstract

The characterization of density fluctuations in systems of interacting particles is of fundamental importance in the physical sciences. We present a formalism for studying local density fluctuations in two special subvolumes (centered around either a reference particle or some arbitrary point in the system) termed {ital particle} and {ital void} regions, respectively. We present formal expressions for the probability, as well as the moments, associated with finding exactly {ital n} particles inside of either of these subvolumes. Furthermore, we derive the relationship between the probability functions and closely related quantities of interest, such as the nth nearest-neighbor distribution functions and the {ital n}-particle conditional pair distribution functions associated with each region. We solve for these quantities exactly in the one-dimensional hard-rod system. The methods developed for studying the hard-rod fluid are applicable for studying a wide class of one-dimensional systems. {copyright} {ital 1998} {ital The American Physical Society}