Global well-posedness in a Hartree-Fock model for graphene
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912376368922624 |
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| author | Borrelli, William Morellini, Umberto |
| author_facet | Borrelli, William Morellini, Umberto |
| contents | Graphene is a monolayer graphitic film in which electrons behave like two-dimensional Dirac fermions without mass. Its study has attracted a wide interest in the domain of condensed matter physics. In particular, it represents an ideal system to test the comprehension of 2D massless relativistic particles in a laboratory, the Fermi velocity being 300 times smaller than the speed of light. In this work, we present a global well-posedness result for graphene in the Hartree- Fock approximation. The model allows to describe the time evolution of graphene in the presence of external time-dependent electric potentials, such as those induced by local charge defects in the monolayer of carbon atoms. Our approach is based on a well established non-perturbative framework originating from the study of three-dimensional quantum electrodynamics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_14028 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global well-posedness in a Hartree-Fock model for graphene Borrelli, William Morellini, Umberto Mathematical Physics Mesoscale and Nanoscale Physics Analysis of PDEs Graphene is a monolayer graphitic film in which electrons behave like two-dimensional Dirac fermions without mass. Its study has attracted a wide interest in the domain of condensed matter physics. In particular, it represents an ideal system to test the comprehension of 2D massless relativistic particles in a laboratory, the Fermi velocity being 300 times smaller than the speed of light. In this work, we present a global well-posedness result for graphene in the Hartree- Fock approximation. The model allows to describe the time evolution of graphene in the presence of external time-dependent electric potentials, such as those induced by local charge defects in the monolayer of carbon atoms. Our approach is based on a well established non-perturbative framework originating from the study of three-dimensional quantum electrodynamics. |
| title | Global well-posedness in a Hartree-Fock model for graphene |
| topic | Mathematical Physics Mesoscale and Nanoscale Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2411.14028 |