<div class="csl-bib-body">
<div class="csl-entry">Barletti, L., Holzinger, P., & Jüngel, A. (2022). Formal derivation of quantum drift-diffusion equations with spin-orbit interaction. <i>Kinetic and Related Models</i>, <i>15</i>(2), 257–282. https://doi.org/10.3934/krm.2022007</div>
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dc.identifier.issn
1937-5093
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/139290
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dc.description.abstract
Quantum drift-diffusion equations for a two-dimensional electron gas with spin-orbit interactions of Rashba type are formally derived from a collisional Wigner equation. The collisions are modeled by a Bhatnagar—Gross— Krook-type operator describing the relaxation of the electron gas to a local equilibrium that is given by the quantum maximum entropy principle. Because of non-commutativity properties of the operators, the standard diffusion scaling cannot be used in this context, and a hydrodynamic time scaling is required. A Chapman—Enskog procedure leads, up to first order in the relaxation time, to a system of nonlocal quantum drift-diffusion equations for the charge density and spin vector densities. Local equations including the Bohm potential are obtained in the semiclassical expansion up to second order in the scaled Planck constant. The main novelty of this work is that all spin components are considered, while previous models only consider special spin directions.
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dc.description.sponsorship
European Commission
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dc.description.sponsorship
Fonds zur Förderung der wissenschaftlichen Forschung (FWF)
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dc.description.sponsorship
Fonds zur Förderung der wissenschaftlichen Forschung (FWF)
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dc.description.sponsorship
Fonds zur Förderung der wissenschaftlichen Forschung (FWF)
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dc.description.sponsorship
Fonds zur Förderung der wissenschaftlichen Forschung (FWF)
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dc.language.iso
en
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dc.publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
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dc.relation.ispartof
Kinetic and Related Models
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dc.subject
Bohm potential
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dc.subject
diffusion limit
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dc.subject
quantum maximum entropy principle
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dc.subject
semiclassical model
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dc.subject
spin-orbit interaction
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dc.subject
Wigner-Boltzmann equation
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dc.title
Formal derivation of quantum drift-diffusion equations with spin-orbit interaction