The search for NLS ground states on a hybrid domain: Motivations, methods, and results
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916926236655616 |
|---|---|
| author | Adami, Riccardo Boni, Filippo Carlone, Raffaele Tentarelli, Lorenzo |
| author_facet | Adami, Riccardo Boni, Filippo Carlone, Raffaele Tentarelli, Lorenzo |
| contents | We discuss the problem of establishing the existence of the Ground States for the subcritical focusing Nonlinear Schrödinger energy on a domain made of a line and a plane intersecting at a point. The problem is physically motivated by the experimental realization of hybrid traps for Bose-Einstein Condensates, that are able to concentrate the system on structures close to the domain we consider. In fact, such a domain approximates the trap as the temperature approaches the absolute zero. The spirit of the paper is mainly pedagogical, so we focus on the formulation of the problem and on the explanation of the result, giving references for the technical points and for the proofs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_07843 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The search for NLS ground states on a hybrid domain: Motivations, methods, and results Adami, Riccardo Boni, Filippo Carlone, Raffaele Tentarelli, Lorenzo Analysis of PDEs Mathematical Physics Functional Analysis 35R02, 81Q35, 35Q55, 35Q40, 35B07, 35B09, 35R99 We discuss the problem of establishing the existence of the Ground States for the subcritical focusing Nonlinear Schrödinger energy on a domain made of a line and a plane intersecting at a point. The problem is physically motivated by the experimental realization of hybrid traps for Bose-Einstein Condensates, that are able to concentrate the system on structures close to the domain we consider. In fact, such a domain approximates the trap as the temperature approaches the absolute zero. The spirit of the paper is mainly pedagogical, so we focus on the formulation of the problem and on the explanation of the result, giving references for the technical points and for the proofs. |
| title | The search for NLS ground states on a hybrid domain: Motivations, methods, and results |
| topic | Analysis of PDEs Mathematical Physics Functional Analysis 35R02, 81Q35, 35Q55, 35Q40, 35B07, 35B09, 35R99 |
| url | https://arxiv.org/abs/2404.07843 |