2019/09/17 by Jeff Murugan, Murugan, Jeff, Jonathan P. Shock +3 · 1 citation
Mathematics · Physics and Astronomy · #FOS: Physical sciences #High Energy Astrophysical Phenomena (astro-ph.HE) #High Energy Physics - Theory (hep-th) #Quantum Gases (cond-mat.quant-gas) #Quantum Mechanics and Non-Hermitian Physics #Quantum optics and atomic interactions #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1909.08042
openalex publication_date 2019/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In a recent article, we were motivated by the question of whether any of the remarkable condensed matter phenomena, such as the quantum Hall effect (QHE), the Integer quantum Hall effect (IQHE) etc., could potentially be observed in the extreme astrophysical environments of neutron stars. As a prequel to that work, and with the aim of understanding better the role of the geometry of the conducting surface on the structure of Landau levels, in this article we study the quantum dynamics of a quantum particle on a squashed sphere. More specifically, we study the dynamics of a single particle on an oblate squashed Haldane sphere i.e. a 2-sphere enclosing a single magnetic monopole at its center. While several features of the conventional Haldane sphere persist, by numerically solving the Schrodinger equation in this background, we find that the particle becomes increasingly localised in a band between the equator and the poles, with a corresponding increase of the eccentricity of the spheroid.