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 δ-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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| Formato: | artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Recursos: | Universidad de Cantabria (UC) |
| Repositorio: | UCrea Repositorio Abierto de la Universidad de Cantabria |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.unican.es:10902/29162 |
| Acesso em linha: | https://hdl.handle.net/10902/29162 |
| Access Level: | acceso abierto |
| Palavra-chave: | Dirac operator Quantum-dot Lorentz-scalar δ-shell Boundary conditions Selfadjoint operator Conformal map Corner domains |
| Resumo: | We investigate the self-adjointness of the two-dimensional Dirac operator D, with quantum-dot and Lorentz-scalar δ-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 isthen translated to general domains by a coordinate transformation. |
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