Self-adjointness of two-dimensional Dirac operators on corner domains
We investigate the self-adjointness of the two-dimensional Dirac operator D, with quantum-dot and Lorentz-scalar i-shell boundary conditions, on piecewise C2 domains (with finitely many corners). For both models, we prove the existence of a unique self-adjoint realization whose domain is included in...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Basque Center for Applied Mathematics (BCAM) |
| Repositorio: | BIRD. BCAM's Institutional Repository Data |
| OAI Identifier: | oai:bird.bcamath.org:20.500.11824/1450 |
| Acceso en línea: | http://hdl.handle.net/20.500.11824/1450 |
| Access Level: | acceso abierto |
| Palabra clave: | Boundary conditions Conformal map Corner domains Dirac operator Lorentz-scalar i-shell Quantum-dot Selfadjoint operator |
| Sumario: | We investigate the self-adjointness of the two-dimensional Dirac operator D, with quantum-dot and Lorentz-scalar i-shell boundary conditions, on piecewise C2 domains (with finitely many corners). For both models, we prove the existence of a unique self-adjoint realization whose domain is included in the Sobolev space H1=2, the formal form domain of the free Dirac operator. The main part of our paper consists of a description of the domain of the adjoint operator D in terms of the domain of D and the set of harmonic functions that verify some mixed boundary conditions. Then, we give a detailed study of the problem on an infinite sector, where explicit computations can be made: we find the self-adjoint extensions for this case. The result is then translated to general domains by a coordinate transformation. |
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