The search for NLS ground states on a hybrid domain: Motivations, methods, and results

Abstract

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.

arXiv commentContribution 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 Schrödinger, ground states, delta interaction. Minor revisions have been made with respect to the previous version

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Cited by in corpus (1)

• Normalized NLS ground states on a double plane hybrid