The ``electromagnetic Wigner equation for an electron with spin

DOI10.1007/BF00945803zbMath0701.35130OpenAlexW1997488435MaRDI QIDQ914069

Anton Arnold, Herbert Steinrück

Publication date: 1989

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00945803

zbMATH Keywords

uniquenessWigner equationExistenceclassical limit\(L^{\infty }\)-estimateelectron with spin

Mathematics Subject Classification ID

Groups and semigroups of linear operators (47D03) Electromagnetic interaction; quantum electrodynamics (81V10) PDEs in connection with quantum mechanics (35Q40) Initial value problems for PDEs with pseudodifferential operators (35S10)

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Spatial resolution of different discretizations over long-time for the Dirac equation with small potentials ⋮ Phase-space methods for the spin dynamics in condensed matter systems ⋮ Scalar quantum kinetic theory for spin-1/2 particles: mean field theory ⋮ The Schrödinger-Newton equations beyond Newton ⋮ Explicit and structure-preserving exponential wave integrator Fourier pseudo-spectral methods for the Dirac equation in the simultaneously massless and nonrelativistic regime ⋮ The Magnetic Liouville Equation as a Semiclassical Limit ⋮ Semiclassical limit of the Schrödinger-Poisson-Landau-Lifshitz-Gilbert system ⋮ Magnetoacoustic solitons in dense astrophysical electron-positron-ion plasmas ⋮ The influence of Landau quantization on the propagation of solitary structures in collisional plasmas ⋮ Numerical methods and comparison for the Dirac equation in the nonrelativistic limit regime ⋮ Wigner Envelope Functions for Electron Transport in Semiconductor Devices ⋮ Error bounds of the finite difference time domain methods for the Dirac equation in the semiclassical regime ⋮ A fourth-order compact time-splitting Fourier pseudospectral method for the Dirac equation

Cites Work

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• Semigroups of linear operators and applications to partial differential equations
• On the equivalence of the Schrödinger and the quantum Liouville equations
• PSEUDODIFFERENCE OPERATORS AND THEIR GREEN'S FUNCTIONS
• Local existence of solutions of the vlasov‐maxwell equations and convergence to the vlasov‐poisson equations for infinite light velocity
• An Analysis of the Quantum Liouville Equation
• Schrödinger operators with singular magnetic vector potentials

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