Dissertation/ Thesis
Spectral gap of generalized MIT bag models
| Τίτλος: | Spectral gap of generalized MIT bag models |
|---|---|
| Συγγραφείς: | Duran Lamiel, Joaquim |
| Συνεισφορές: | Mas Blesa, Albert, Universitat Politècnica de Catalunya. Departament de Matemàtiques, Centre de Recerca Matemàtica |
| Πηγή: | UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) |
| Στοιχεία εκδότη: | Universitat Politècnica de Catalunya, 2024. |
| Έτος έκδοσης: | 2024 |
| Θεματικοί όροι: | resolvent convergence, Teoria dels, Dirac operator, Quàntums, Teoria dels, Classificació AMS::47 Operator theory::47A General theory of linear operators, Quàntums, Classificació AMS::81 Quantum theory::81Q General mathematical topics and methods in quantum theory, spectral theory, Teoria espectral (Matemàtica), Quantum theory, shape optimization, Spectral theory (Mathematics), MIT bag model, Classificació AMS::35 Partial differential equations::35Q Equations of mathematical physics and other areas of application, Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals, Classificació AMS::35 Partial differential equations::35P Spectral theory and eigenvalue problems for partial differential operators |
| Περιγραφή: | We study some spectral properties of generalized MIT bag models. These are a family of Dirac operators $\{H_\tau\}_{\tau \in \mathbb R\cup \{-\infty, +\infty\}}$ used in the field of relativistic quantum mechanics to model confinement of quarks in hadrons, and their energies are related with the spectra of such operators. Their lowest positive eigenvalue is of special interest, and in \cite{Mas2022} it was conjectured that it is minimal for a ball among all domains of the same volume. In this work we prove that the conjecture holds true for corona domains of relatively small hole. Moreover, motivated by some open questions presented in \cite{Mas2022}, in this work we also study the convergence in several resolvent senses of $H_\tau$ as $\tau$ varies. More specifically, we show strong resolvent convergence of $H_\tau$ to $H_{\pm \infty}$ as $\tau \to \pm \infty$, we justify that one cannot improve this to norm resolvent convergence as $\tau \to \pm \infty$, and we show norm resolvent convergence of $H_\tau$ to $H_{\tau_0}$ as $\tau \to \tau_0$, for $\tau_0\in \mathbb R$. These results are new and will be sent for publication in an indexed journal. |
| Τύπος εγγράφου: | Master thesis |
| Περιγραφή αρχείου: | application/pdf |
| Γλώσσα: | English |
| Σύνδεσμος πρόσβασης: | https://hdl.handle.net/2117/400748 |
| Rights: | CC BY NC ND |
| Αριθμός Καταχώρησης: | edsair.dedup.wf.002..33c6f29e60072739bc1cc3db334f1c8d |
| Βάση Δεδομένων: | OpenAIRE |
| Η περιγραφή δεν είναι διαθέσιμη |