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.

References in corpus (3)

• Theory of Bose-Einstein condensation in trapped gases
• Ground-State Properties of Magnetically Trapped Bose-Condensed Rubidium Gas
• Bose-Einstein condensation in variable dimensionality

Cited by in corpus (6)

• Manipulation of Molecules with Electromagnetic Fields
• Analytic, Group-Theoretic Density Profiles for Confined, Correlated N-Body Systems
• On the Use of Group Theoretical and Graphical Techniques toward the Solution of the General N-body Problem
• Normal modes for N identical particles: A study of the evolution of collective behavior from few-body to many-body
• Analytic normal mode frequencies for N identical particles: The microscopic dynamics underlying the emergence and stability of excitation gaps from BCS to unitarity
• Generalization of the Fermi Pseudopotential