Generalized one-dimensional nonpolynomial Schrödinger equation for Bose-Einstein condensates with generic transverse confinement
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908664827215872 |
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| author | Basso, Andréia M. Cardoso, Wesley B. |
| author_facet | Basso, Andréia M. Cardoso, Wesley B. |
| contents | This work presents a dimensional reduction of Bose-Einstein condensates confined by generalized transverse potentials, parametrized by an exponent $n$. Starting from the three-dimensional Gross-Pitaevskii equation, we employ a variational ansatz to derive an effective one-dimensional nonpolynomial Schrödinger equation, which self-consistently determines the transverse width dynamics. The model generalizes existing formalisms for cigar- and funnel-shaped geometries. We validate the approach through comprehensive numerical tests, demonstrating excellent agreement with full 3D simulations for ground-state properties across various interaction regimes. Finally, real-time simulations of matter-wave scattering at potential barriers verify the model's dynamical robustness, successfully replicating the spatiotemporal evolution and energy-dependent transmission characteristics observed in full 3D calculations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_14973 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized one-dimensional nonpolynomial Schrödinger equation for Bose-Einstein condensates with generic transverse confinement Basso, Andréia M. Cardoso, Wesley B. Quantum Gases Pattern Formation and Solitons This work presents a dimensional reduction of Bose-Einstein condensates confined by generalized transverse potentials, parametrized by an exponent $n$. Starting from the three-dimensional Gross-Pitaevskii equation, we employ a variational ansatz to derive an effective one-dimensional nonpolynomial Schrödinger equation, which self-consistently determines the transverse width dynamics. The model generalizes existing formalisms for cigar- and funnel-shaped geometries. We validate the approach through comprehensive numerical tests, demonstrating excellent agreement with full 3D simulations for ground-state properties across various interaction regimes. Finally, real-time simulations of matter-wave scattering at potential barriers verify the model's dynamical robustness, successfully replicating the spatiotemporal evolution and energy-dependent transmission characteristics observed in full 3D calculations. |
| title | Generalized one-dimensional nonpolynomial Schrödinger equation for Bose-Einstein condensates with generic transverse confinement |
| topic | Quantum Gases Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2511.14973 |