Ground State Asymptotics of a Dilute, Rotating Gas

TL;DR

This paper studies the ground state behavior of a dilute, rotating Bose gas in three dimensions, revealing how symmetry breaking affects the accuracy of the Gross-Pitaevskii approximation in the GP limit.

Contribution

It demonstrates that a modified GP functional accurately describes the energy and density matrices for the absolute ground state regardless of symmetry breaking, but only for the bosonic ground state when symmetry is unbroken.

Findings

Modified GP functional captures energy and density matrices for absolute ground state.

Accuracy of GP approximation depends on symmetry breaking in the bosonic ground state.

Different behaviors observed for absolute and bosonic ground states in the GP limit.

Abstract

We investigate the ground state properties of a gas of interacting particles confined in an external potential in three dimensions and subject to rotation around an axis of symmetry. We consider the so-called Gross-Pitaevskii (GP) limit of a dilute gas. Analyzing both the absolute and the bosonic ground state of the system we show, in particular, their different behavior for a certain range of parameters. This parameter range is determined by the question whether the rotational symmetry in the minimizer of the GP functional is broken or not. For the absolute ground state, we prove that in the GP limit a modified GP functional depending on density matrices correctly describes the energy and reduced density matrices, independent of symmetry breaking. For the bosonic ground state this holds true if and only if the symmetry is unbroken.