Mathematical analysis of a Mateo-Delgado model for cigar-shaped Bose-Einstein condensates
Mathematical analysis of a Mateo-Delgado model
DOI:
https://doi.org/10.5540/tcam.2026.027.e01918Keywords:
Bose-Einstein condensates, stability of ground states, analytical approximate formulae, repulsive interatomic interactionsAbstract
In this paper we present a mathematical analysis of one-dimensional effective model proposed by A.M.~Mateo and V.~Delgado concerning Bose-Einstein condensates in the presence of harmonic confinement. Among the properties presented, we 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 $\lambda$, which is a parameter 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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Copyright (c) 2026 R. Cipolatti, Y. M. Lira, G. Saisse
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