Phase-space localization at the lowest Landau level
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.
Keywords
Cite
@article{arxiv.2407.07675,
title = {Phase-space localization at the lowest Landau level},
author = {Ben Craps and Marine De Clerck and Oleg Evnin and Maxim Pavlov},
journal= {arXiv preprint arXiv:2407.07675},
year = {2025}
}
Comments
v2: published version; MATLAB codes available at https://doi.org/10.5281/zenodo.12704876