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arXiv · 2411.19157

Mathematical analysis of a Mu\~noz-Delgado model for cigar-shaped Bose-Einstein condensates

Rolci Cipolatti·Yuri M. Lira·Giovanni L. G. Saisse
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Abstract

In this paper we present mathematical analysis of one-dimensional effective models proposed in [\cite{MunozDelgado}] 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 formul\ae\ for the minimal energy $E_{\mn}$ and the associate chemical potential $\mu$ as functions of a parameter $\lambda$, 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.

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Rolci Cipolatti, Yuri M. Lira, Giovanni L. G. Saisse. 2024-11-28. Mathematical analysis of a Mu\~noz-Delgado model for cigar-shaped Bose-Einstein condensates. https://arxiv.org/abs/2411.19157

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