Radiative transport in a periodic structure with band crossings
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916472109924352 |
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| author | Qi, Kunlun Wang, Li Watson, Alexander B. |
| author_facet | Qi, Kunlun Wang, Li Watson, Alexander B. |
| contents | We use the Wigner transformation and asymptotic analysis to systematically derive the semi-classical model for the Schrödinger equation in arbitrary spatial dimensions, with any periodic structure. Our particular emphasis lies in addressing the \textit{diabatic} effect, i.e., the impact of Bloch band crossings. We consider both deterministic and random scenarios. In the former case, we derive a coupled Liouville system, revealing lower-order interactions among different Bloch bands. In the latter case, a coupled system of radiative transport equations emerges, with the scattering cross-section induced by the random inhomogeneities. As a specific application, we deduce the effective dynamics of a wave packet in graphene with randomness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_06828 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Radiative transport in a periodic structure with band crossings Qi, Kunlun Wang, Li Watson, Alexander B. Mathematical Physics Analysis of PDEs Quantum Physics Primary: 82C70, 35Q99, 35R60, Secondary: 74A40, 74E05, 74Q10 We use the Wigner transformation and asymptotic analysis to systematically derive the semi-classical model for the Schrödinger equation in arbitrary spatial dimensions, with any periodic structure. Our particular emphasis lies in addressing the \textit{diabatic} effect, i.e., the impact of Bloch band crossings. We consider both deterministic and random scenarios. In the former case, we derive a coupled Liouville system, revealing lower-order interactions among different Bloch bands. In the latter case, a coupled system of radiative transport equations emerges, with the scattering cross-section induced by the random inhomogeneities. As a specific application, we deduce the effective dynamics of a wave packet in graphene with randomness. |
| title | Radiative transport in a periodic structure with band crossings |
| topic | Mathematical Physics Analysis of PDEs Quantum Physics Primary: 82C70, 35Q99, 35R60, Secondary: 74A40, 74E05, 74Q10 |
| url | https://arxiv.org/abs/2402.06828 |