A quantum-transport model for semiconductors : the Wigner-Poisson problem on a bounded Brillouin zone

DOI10.1051/m2an/1990240606971zbMath0742.35046OpenAlexW2585005819MaRDI QIDQ4713864

Pierre Degond, Peter Alexander Markowich

Publication date: 25 June 1992

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/193612

zbMATH Keywords

uniquenessglobal existencePoisson equationquantum Liouville equationself-consistent potentialsemiconductor crystal latticetransport of electrons in semiconductors

Mathematics Subject Classification ID

PDEs in connection with quantum mechanics (35Q40)

Related Items

Quantum forced oscillator via Wigner transform ⋮ A mathematical analysis of quantum transport in three-dimensional crystals ⋮ Numerical Analysis of the Deterministic Particle Method Applied to the Wigner Equation ⋮ On absorbing boundary conditions for quantum transport equations ⋮ Velocity Averaging and Hölder Regularity for Kinetic Fokker--Planck Equations with General Transport Operators and Rough Coefficients

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Semigroups of linear operators and applications to partial differential equations
• Regularity of the moments of the solution of a transport equation
• Semi-classical asymptotics in solid state physics
• The Wigner-Poisson problem in a crystal
• On the equivalence of the Schrödinger and the quantum Liouville equations
• An Analysis of the Quantum Liouville Equation