Phase-space localization at the lowest Landau level

TL;DR

This paper investigates how weak interactions in bosonic systems at the lowest Landau level lead to phase-space localization of quantum states, revealing emergent localized structures in classical phase space.

Contribution

It introduces a phase-space analysis of bosonic states at the lowest Landau level, highlighting localization effects induced by interactions.

Findings

Interactions lift degeneracy of energy levels.

Localized Husimi distributions appear around low-dimensional surfaces.

Localization emerges due to interactions in phase space.

Abstract

We consider bosons with weak contact interactions in a harmonic trap and focus on states at the lowest Landau level. Motivated by the known nontrivial phase-space topography of the energy functional of the corresponding Gross-Pitaevskii equation, we explore Husimi distributions of quantum energy eigenstates in the classical phase space of the Schroedinger field. With interactions turned off, the energy levels are highly degenerate and the Husimi distributions do not manifest any particular localization properties. With interactions turned on, the degeneracy is lifted, and a selection of energy levels emerges whose Husimi distributions are localized around low-dimensional surfaces in the phase space.