Analytic, Group-Theoretic Density Profiles for Confined, Correlated N-Body Systems

TL;DR

This paper derives an analytic density profile for confined, correlated N-body quantum systems using group-theoretic dimensional perturbation theory, with application to Bose-Einstein condensates, advancing beyond-mean-field methods.

Contribution

It introduces a novel analytic method combining group theory and dimensional perturbation theory to obtain density profiles for strongly correlated confined quantum systems.

Findings

Derived lowest-order analytic density profile for N-body systems

Applied the method to Bose-Einstein condensates

Demonstrated the approach's applicability across interaction regimes

Abstract

Confined quantum systems involving $N$ identical interacting particles are to be found in many areas of physics, including condensed matter, atomic and chemical physics. A beyond-mean-field perturbation method that is applicable, in principle, to weakly, intermediate, and strongly-interacting systems has been set forth by the authors in a previous series of papers. Dimensional perturbation theory was used, and in conjunction with group theory, an analytic beyond-mean-field correlated wave function at lowest order for a system under spherical confinement with a general two-body interaction was derived. In the present paper, we use this analytic wave function to derive the corresponding lowest-order, analytic density profile and apply it to the example of a Bose-Einstein condensate.