Mathematical analysis of a Muñoz-Delgado model for cigar-shaped Bose-Einstein condensates
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916505512312832 |
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| author | Cipolatti, Rolci Lira, Yuri M. Saisse, Giovanni L. G. |
| author_facet | Cipolatti, Rolci Lira, Yuri M. Saisse, Giovanni L. G. |
| contents | 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 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_19157 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mathematical analysis of a Muñoz-Delgado model for cigar-shaped Bose-Einstein condensates Cipolatti, Rolci Lira, Yuri M. Saisse, Giovanni L. G. Analysis of PDEs Other Condensed Matter 35 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 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. |
| title | Mathematical analysis of a Muñoz-Delgado model for cigar-shaped Bose-Einstein condensates |
| topic | Analysis of PDEs Other Condensed Matter 35 |
| url | https://arxiv.org/abs/2411.19157 |