Rizzello, Giuseppe (2026) Beyond the Winter Model. [Tesi di dottorato]
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| Tipologia del documento: | Tesi di dottorato |
|---|---|
| Lingua: | English |
| Titolo: | Beyond the Winter Model |
| Autori: | Autore Email Rizzello, Giuseppe giuseppe.rizzello@unina.it |
| Data: | 9 Giugno 2026 |
| Numero di pagine: | 169 |
| Istituzione: | Università degli Studi di Napoli Federico II |
| Dipartimento: | Matematica e Applicazioni "Renato Caccioppoli" |
| Dottorato: | Matematica e Applicazioni |
| Ciclo di dottorato: | 38 |
| Coordinatore del Corso di dottorato: | nome email Nitsch, Carlo carlo.nitsch@unina.it |
| Tutor: | nome email Carlone, Raffaele [non definito] |
| Data: | 9 Giugno 2026 |
| Numero di pagine: | 169 |
| Parole chiave: | Winter model; Quantum resonances; Singular interactions; Hybrid quantum systems; Nonlinear Schrödinger equations; Ground states |
| Settori scientifico-disciplinari del MIUR: | Area 01 - Scienze matematiche e informatiche > MAT/05 - Analisi matematica Area 01 - Scienze matematiche e informatiche > MAT/07 - Fisica matematica |
| Informazioni aggiuntive: | Ciclo 38 |
| Depositato il: | 17 Giu 2026 21:03 |
| Ultima modifica: | 12 Ago 2026 05:37 |
| URI: | https://www.fedoa.unina.it/id/eprint/16034 |
Abstract
This thesis investigates several extensions of the Winter model, a quantum system with singular interactions that provides a paradigmatic framework for the study of resonances and spectral properties. The first part is devoted to the analysis of the classical Winter model in both three and two dimensions, including the characterization of its spectrum and resonances. The study is then extended to modified configurations involving an additional point interaction at the origin. A geometric perturbation of the two-dimensional Winter model, obtained by deforming the interaction support, is also considered, and its effect on the spectral properties of the system is analyzed. A hybrid model coupling a planar Winter system with a half-line through self-adjoint extension techniques is introduced and studied. The second part of the thesis concerns nonlinear Schrödinger equations associated with the two-dimensional Winter model with an additional point interaction and with the hybrid model. Variational methods are employed to investigate the existence and properties of ground states under mass constraints.
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