Barletti, L., Holzinger, P., & Jüngel, A. (2022). Formal derivation of quantum drift-diffusion equations with spin-orbit interaction. Kinetic and Related Models, 15(2), 257–282. https://doi.org/10.3934/krm.2022007
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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Project title:
Emergente Netzwerkstrukturen und neuromorphische Anwendungen: 101018153 (European Commission) Derivation and analysis of cross-diffusion systems: P 30000-N32 (Fonds zur Förderung der wissenschaftlichen Forschung (FWF)) Multikomponentensysteme mit unvollständiger Diffusion: P 33010-N (Fonds zur Förderung der wissenschaftlichen Forschung (FWF)) Langzeitverhalten von diskreten dissipativen Systemen: F6503-N36 (Fonds zur Förderung der wissenschaftlichen Forschung (FWF)) Doktoratskolleg "Dissipation and Dispersion in Nonlinear Partial Differential Equations": W1245-N25 (Fonds zur Förderung der wissenschaftlichen Forschung (FWF))
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Project (external):
Italian National Group for Mathematical Physics (INdAM-GNFM)
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Research Areas:
Quantum Modeling and Simulation: 70% Modeling and Simulation: 30%
