2024/11/28 by Rolci Cipolatti, Cipolatti, Rolci, Yuri M. Lira +3
Physics and Astronomy · #35 #Analysis of PDEs (math.AP) #Cold Atom Physics and Bose-Einstein Condensates #FOS: Mathematics #FOS: Physical sciences #Other Condensed Matter (cond-mat.other) #Physics of Superconductivity and Magnetism
paper · pdf · doi:10.48550/arxiv.2411.19157
openalex publication_date 2024/11/28 · openalex created_date 2024/12/05 · openalex updated_date 2026/07/28
In this paper we present mathematical analysis of one-dimensional effective models proposed in [\citeMunozDelgado] concerning Bose-Einstein condensates in the presence of harmonic confinement. Among the demonstrated properties, we can mention: existence, uniqueness, orbital stability, symmetry and gaussian asymptotic decay of ground-state solutions in the repulsive case. We also report formulæ for the minimal energy E\mn and the associate chemical potential μ as functions of a parameter λ, which is related to N (the number of atoms) and/or a (the s-wave scattering length). By considering Taylor's development of the non-quadratic therm of the energy and using appropriate gaussian functions as approximations for the ground state, we present some numerical experiments to illustrate our results.