تقرير
The search for NLS ground states on a hybrid domain: Motivations, methods, and results
| العنوان: | The search for NLS ground states on a hybrid domain: Motivations, methods, and results |
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| المؤلفون: | Adami, Riccardo, Boni, Filippo, Carlone, Raffaele, Tentarelli, Lorenzo |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics Mathematical Physics |
| مصطلحات موضوعية: | Mathematics - Analysis of PDEs, Mathematical Physics, Mathematics - Functional Analysis, 35R02, 81Q35, 35Q55, 35Q40, 35B07, 35B09, 35R99 |
| الوصف: | We discuss the problem of establishing the existence of the Ground States for the subcritical focusing Nonlinear Schr\"odinger 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. Comment: Contribution for the Proceedings of the Summer School of the Puglia Trimester 2023 "Singularities, Asymptotics and Limiting Models". 18 pages, 1 figure. Keywords: hybrids, standing waves, nonlinear Schr\"odinger, ground states, delta interaction. Minor revisions have been made with respect to the previous version |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2404.07843 |
| رقم الأكسشن: | edsarx.2404.07843 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |