Positive-density ground states of the Gross-Pitaevskii equation
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| author | Lewin, Mathieu Nam, Phan Thành |
| author_facet | Lewin, Mathieu Nam, Phan Thành |
| contents | We consider the nonlinear Gross-Pitaevskii equation at positive density, that is, for a bounded solution not tending to 0 at infinity. We focus on infinite ground states, which are by definition minimizers of the energy under local perturbations. When the Fourier transform of the interaction potential takes negative values we prove the existence of a phase transition at high density, where the constant solution ceases to be a ground state. The analysis requires mixing techniques from elliptic PDE theory and statistical mechanics, in order to deal with a large class of interaction potentials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_03495 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Positive-density ground states of the Gross-Pitaevskii equation Lewin, Mathieu Nam, Phan Thành Mathematical Physics Analysis of PDEs We consider the nonlinear Gross-Pitaevskii equation at positive density, that is, for a bounded solution not tending to 0 at infinity. We focus on infinite ground states, which are by definition minimizers of the energy under local perturbations. When the Fourier transform of the interaction potential takes negative values we prove the existence of a phase transition at high density, where the constant solution ceases to be a ground state. The analysis requires mixing techniques from elliptic PDE theory and statistical mechanics, in order to deal with a large class of interaction potentials. |
| title | Positive-density ground states of the Gross-Pitaevskii equation |
| topic | Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2310.03495 |