Radiative transport in a periodic structure with band crossings
- URL: http://arxiv.org/abs/2402.06828v1
- Date: Fri, 9 Feb 2024 23:34:32 GMT
- Title: Radiative transport in a periodic structure with band crossings
- Authors: Kunlun Qi and Li Wang and Alexander B. Watson
- Abstract summary: We derive the semi-classical model for the Schr"odinger equation in arbitrary spatial dimensions.
We consider both deterministic and random scenarios.
As a specific application, we deduce the effective dynamics of a wave packet in graphene with randomness.
- Score: 52.24960876753079
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We use the Wigner transformation and asymptotic analysis to systematically
derive the semi-classical model for the Schr\"{o}dinger 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.
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