NDLI: Isothermal Quantum Hydrodynamics: Derivation, Asymptotic Analysis, and Simulation

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Mhats, F. Degond, P. Gallego, S.
Copyright Year	2007
Abstract	This article is devoted to the reformulation of an isothermal version of the quantum hydrodynamic model derived by Degond and Ringhofer in J. Statist. Phys., 112 2003, pp. 587628 which will be referred to as the quantum Euler system. We write the model under a simpler differential form. The derivation is based on an appropriate use of commutators. Starting from the quantum Liouville equation, the system of moments is closed by a density operator which minimizes the quantum free energy. Some properties of the model are then exhibited, and most of them rely on a gauge invariance property of the system. Several simplifications of the model are also written for the special case of irrotational flows. The second part of the paper is devoted to a formal analysis of the asymptotic behavior of the quantum Euler system in three situations: at the semiclassical limit, at the zerotemperature limit, and at a diffusive limit. The remarkable fact is that in each case we recover a known model: respectively, the isothermal Euler system, the Madelung equations, and the entropic quantum driftdiffusion model. Finally, we give in the third part some preliminary numerical simulations.
Starting Page	246
Ending Page	272
Page Count	27
File Format	PDF
ISSN	15403459
DOI	10.1137/06067153X
e-ISSN	15403467
Journal	Multiscale Modeling & Simulation (MMSUBT)
Issue Number	1
Volume Number	6
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2007-04-24
Access Restriction	Subscribed
Subject Keyword	entropy minimization numerical simulations Semiconductors Phase-space methods including Wigner distributions, etc. Madelung equations asymptotic analysis quantum Euler quantum moment hydrodynamics Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics Canonical quantization, commutation relations and statistics density matrix entropic quantum driftdiffusion quantum Liouville equation Many-body theory; quantum Hall effect Quantum dynamics and nonequilibrium statistical mechanics Transport processes local equilibria
Content Type	Text
Resource Type	Article
Subject	Chemistry Ecological Modeling Physics and Astronomy Computer Science Applications Modeling and Simulation

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