Convergence of generalized MIT bag models to Dirac operators with zigzag boundary conditions
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908459512889344 |
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| author | Duran, Joaquim Mas, Albert |
| author_facet | Duran, Joaquim Mas, Albert |
| contents | This work addresses the resolvent convergence of generalized MIT bag operators to Dirac operators with zigzag type boundary conditions. We prove that the convergence holds in strong but not in norm resolvent sense. Moreover, we show that the only obstruction for having norm resolvent convergence is the existence of an eigenvalue of infinite multiplicity for the limiting operator. More precisely, we prove the convergence of the resolvents in operator norm once projected into the orthogonal of the corresponding eigenspace. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_17057 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convergence of generalized MIT bag models to Dirac operators with zigzag boundary conditions Duran, Joaquim Mas, Albert Analysis of PDEs Mathematical Physics 35P05, 35Q40 (Primary), 47A10, 81Q10 (Secondary) This work addresses the resolvent convergence of generalized MIT bag operators to Dirac operators with zigzag type boundary conditions. We prove that the convergence holds in strong but not in norm resolvent sense. Moreover, we show that the only obstruction for having norm resolvent convergence is the existence of an eigenvalue of infinite multiplicity for the limiting operator. More precisely, we prove the convergence of the resolvents in operator norm once projected into the orthogonal of the corresponding eigenspace. |
| title | Convergence of generalized MIT bag models to Dirac operators with zigzag boundary conditions |
| topic | Analysis of PDEs Mathematical Physics 35P05, 35Q40 (Primary), 47A10, 81Q10 (Secondary) |
| url | https://arxiv.org/abs/2403.17057 |