A new derivation of the quantum Navier-Stokes equations in the Wigner-Fokker-Planck approach

DOI10.1007/s10955-011-0388-3zbMath1238.82024OpenAlexW2048224141MaRDI QIDQ658510

José Luis López, Jesús Montejo-Gámez, Ansgar Jüngel

Publication date: 12 January 2012

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10955-011-0388-3

zbMATH Keywords

density matrixcollision operatormoment methodquantum Navier-Stokes equationlocal gauge transformationquantum Fokker-Planck equationWigner-Weyl transform

Mathematics Subject Classification ID

Flows in porous media; filtration; seepage (76S05) Navier-Stokes equations (35Q30) PDEs in connection with quantum mechanics (35Q40) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Quantum dynamics and nonequilibrium statistical mechanics (general) (82C10) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30) Quantum hydrodynamics and relativistic hydrodynamics (76Y05)

Related Items (9)

Exponential decay in time of density of one-dimensional quantum Navier-Stokes equations ⋮ On the Lagrangian structure of quantum fluid models ⋮ A benchmark study of the signed-particle Monte Carlo algorithm for the Wigner equation ⋮ An intrinsically hydrodynamic approach to multidimensional QHD systems ⋮ Stability of a one-dimensional full viscous quantum hydrodynamic system ⋮ On the blowing up of solutions to one-dimensional quantum Navier-Stokes equations ⋮ Relaxation limit from the quantum Navier-Stokes equations to the quantum drift-diffusion equation ⋮ Genuine hydrodynamic analysis to the 1-D QHD system: existence, dispersion and stability ⋮ On the derivation and mathematical analysis of some quantum–mechanical models accounting for Fokker–Planck type dissipation: Phase space, Schrödinger and hydrodynamic descriptions

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