Thinking outside the box: the uniform electron gas on a hypersphere

TL;DR

This paper explores a novel model of a homogeneous electron gas confined to a hypersphere, deriving high-density energy expansions and showing their equivalence to traditional jellium in the large system limit.

Contribution

It introduces a hyperspherical electron gas model and derives its energy expansion, connecting it to standard jellium in the thermodynamic limit.

Findings

High-density energy expansions are derived for the hyperspherical electron gas.

In the limit of large electron number, the energy terms match those of conventional jellium.

The model provides a new perspective on electron confinement and many-body interactions.

Abstract

We discuss alternative homogeneous electron gas systems in which a finite number $n$ of electrons are confined to a $D$-dimensional sphere. We derive the first few terms of the high-density ($r_s\to0$, where $r_s$ is the Seitz radius) energy expansions for these systems and show that, in the thermodynamic limit ($n\to\infty$), these terms become identical to those of $D$-dimensional jellium.