Isothermal Quantum Hydrodynamics: Derivation, Asymptotic Analysis, and Simulation

DOI10.1137/06067153XzbMath1135.82019OpenAlexW1984247081MaRDI QIDQ5454236

Florian Méhats, Samy Gallego, Pierre Degond

Publication date: 28 March 2008

Published in: Multiscale Modeling & Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/06067153x

zbMATH Keywords

density matrixasymptotic analysisnumerical simulationsquantum Liouville equationentropy minimizationlocal equilibriaentropic quantum drift-diffusionMadelung equationsquantum Eulerquantum moment hydrodynamics

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Statistical mechanics of semiconductors (82D37) Many-body theory; quantum Hall effect (81V70) Transport processes in time-dependent statistical mechanics (82C70) Quantum dynamics and nonequilibrium statistical mechanics (general) (82C10) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30) Commutation relations and statistics as related to quantum mechanics (general) (81S05)

Related Items (13)

Constrained minimizers of the von Neumann entropy and their characterization ⋮ A splitting scheme for the quantum Liouville-BGK equation ⋮ Derivation of isothermal quantum fluid equations with Fermi-Dirac and Bose-Einstein statistics ⋮ Effective velocity in compressible Navier-Stokes equations with third-order derivatives ⋮ Diffusive limit of the two-band \(k\cdot p\) model for semiconductors ⋮ The quantum Liouville-BGK equation and the moment problem ⋮ The quantum hydrodynamics system in two space dimensions ⋮ Quasineutral limit for the quantum Navier-Stokes-Poisson equations ⋮ An inverse problem in quantum statistical physics ⋮ On the finite energy weak solutions to a system in quantum fluid dynamics ⋮ Non-uniqueness of weak solutions of the quantum-hydrodynamic system ⋮ Kinetic and Hydrodynamic Models for Multi-Band Quantum Transport in Crystals ⋮ Quantum drift-diffusion modeling of spin transport in nanostructures

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