A POINCARÉ-STEKLOV MAP FOR THE MIT BAG MODEL
| hal.structure.identifier | Université de Bordeaux [UB] | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| hal.structure.identifier | Departamento de Matemáticas [Bilbao] | |
| hal.structure.identifier | Basque Center for Applied Mathematics [BCAM] | |
| dc.contributor.author | BENHELLAL, Badreddine | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | BRUNEAU, Vincent | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| hal.structure.identifier | Universidad del Pais Vasco / Euskal Herriko Unibertsitatea [Espagne] [UPV/EHU] | |
| hal.structure.identifier | Departamento de Matemáticas [Bilbao] | |
| hal.structure.identifier | Université de Bordeaux [UB] | |
| dc.contributor.author | ZREIK, Mahdi | |
| dc.date.accessioned | 2024-04-04T02:40:28Z | |
| dc.date.available | 2024-04-04T02:40:28Z | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191067 | |
| dc.description.abstractEn | The purpose of this paper is to introduce and study Poincaré-Steklov (PS) operators associated to the Dirac operator Dm with the so-called MIT bag boundary condition. In a domain Ω ⊂ R 3 , for a complex number z and for Uz a solution of (Dm − z)Uz = 0, the associated PS operator maps the value of Γ − Uz, the MIT bag boundary value of Uz, to Γ + Uz, where Γ ± are projections along the boundary ∂Ω and (Γ − + Γ +) = t ∂Ω is the trace operator on ∂Ω. In the first part of this paper, we show that the PS operator is a zero-order pseudodifferential operator and give its principal symbol. In the second part, we study the PS operator when the mass m is large, and we prove that it fits into the framework of 1/m-pseudodifferential operators, and we derive some important properties, especially its semiclassical principal symbol. Subsequently, we apply these results to establish a Krein-type resolvent formula for the Dirac operator H M = Dm + M β1 R 3 \Ω for large masses M > 0, in terms of the resolvent of the MIT bag operator on Ω. With its help, the large coupling convergence with a convergence rate of O(M −1) is shown. | |
| dc.language.iso | en | |
| dc.title.en | A POINCARÉ-STEKLOV MAP FOR THE MIT BAG MODEL | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math] | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-03706471 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-03706471v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=BENHELLAL,%20Badreddine&BRUNEAU,%20Vincent&ZREIK,%20Mahdi&rft.genre=preprint |
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