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Schrödinger equation with concentrated nonlinearity

Speaker: 
Riccardo Adami
Institution: 
Politecnico di Torino
Schedule: 
Thursday, May 25, 2023 - 11:00
Location: 
A-134
Abstract: 

A concentrated nonlinearity is a phenomenological model for describing the dynamics of quantum particles in the presence of narrow regions made of nonlinear material or impurities. In other contexts, concentrated nonlinearities appear as singular limits of many-body dynamics. We give a review on recent results about models containing a pointwise nonlinearity. We discuss bound states, blow-up, and criticality. Open problems are also introduced. This is a joint project with Filippo Boni, Raffaele Carlone, Michele Correggi, Alberto Fiorenza, Lorenzo Tentarelli.

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