N identical particles under quantum confinement: A many-body dimensional perturbation theory approach
Abstract
Systems that involve N identical interacting particles under quantum confinement appear throughout many areas of physics, including chemical, condensed matter, and atomic physics. In this paper, we present the methods of dimensional perturbation theory, a powerful set of tools that uses symmetry to yield simple results for studying such many-body systems. We present a detailed discussion of the dimensional continuation of the N-particle Schrodinger equation, the spatial dimension D -> infinity equilibrium (D^0) structure, and the normal-mode (D^{-1}) structure. We use the FG matrix method to derive general, analytical expressions for the many-body normal-mode vibrational frequencies, and we give specific analytical results for three confined N-body quantum systems: the N-electron atom, N-electron quantum dot, and N-atom inhomogeneous Bose-Einstein condensate with a repulsive hardcore potential.
Keywords
Cite
@article{arxiv.cond-mat/0306428,
title = {N identical particles under quantum confinement: A many-body dimensional perturbation theory approach},
author = {B. A. McKinney and M. Dunn and D. K. Watson and J. G. Loeser},
journal= {arXiv preprint arXiv:cond-mat/0306428},
year = {2009}
}