Semiclassical limit of cubic nonlinear Schrödinger equations for mixed states
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914111756959744 |
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| author | Han-Kwan, Daniel Rousset, Frédéric |
| author_facet | Han-Kwan, Daniel Rousset, Frédéric |
| contents | In this work, we study the semiclassical limit of cubic Nonlinear Schrödinger equations for mixed states. We justify the limit to a singular Vlasov equation (in which the force field is proportional to the gradient of the density), for data with finite Sobolev regularity whose velocity profiles satisfy a quantum Penrose stability condition. This latter condition is always satisfied for small data (with a smallness condition independent of the semiclassical parameter) both in the focusing and the defocusing case, and for small perturbations of a large class of physically relevant examples in the defocusing case, such as local Maxwellian-like profiles. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_21313 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Semiclassical limit of cubic nonlinear Schrödinger equations for mixed states Han-Kwan, Daniel Rousset, Frédéric Analysis of PDEs Mathematical Physics In this work, we study the semiclassical limit of cubic Nonlinear Schrödinger equations for mixed states. We justify the limit to a singular Vlasov equation (in which the force field is proportional to the gradient of the density), for data with finite Sobolev regularity whose velocity profiles satisfy a quantum Penrose stability condition. This latter condition is always satisfied for small data (with a smallness condition independent of the semiclassical parameter) both in the focusing and the defocusing case, and for small perturbations of a large class of physically relevant examples in the defocusing case, such as local Maxwellian-like profiles. |
| title | Semiclassical limit of cubic nonlinear Schrödinger equations for mixed states |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2510.21313 |