A hydrodynamic approach to multidimensional dissipation-based Schrödinger models from quantum Fokker-Planck dynamics

DOI10.1016/j.physd.2008.12.006zbMath1160.37430OpenAlexW2086510357MaRDI QIDQ1016240

Jesús Montejo-Gámez, José Luis López

Publication date: 5 May 2009

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physd.2008.12.006

zbMATH Keywords

nonlinear Schrödinger equationsquantum hydrodynamicsdissipative phenomenalogarithmic nonlinearitiesWigner-Fokker-Planck equation

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs in connection with quantum mechanics (35Q40) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) (37N20) Quantum hydrodynamics and relativistic hydrodynamics (76Y05)

Related Items (8)

Universal dynamics for the defocusing logarithmic Schrödinger equation ⋮ Wellposedness of a nonlinear, logarithmic Schrödinger equation of Doebner-Goldin type modeling quantum dissipation ⋮ A new derivation of the quantum Navier-Stokes equations in the Wigner-Fokker-Planck approach ⋮ On a rigorous interpretation of the quantum Schrödinger-Langevin operator in bounded domains with applications ⋮ A quantum approach to Keller-Segel dynamics via a dissipative nonlinear Schrödinger equation ⋮ Global \(H^1\) solvability of the 3D logarithmic Schrödinger equation ⋮ On the derivation and mathematical analysis of some quantum–mechanical models accounting for Fokker–Planck type dissipation: Phase space, Schrödinger and hydrodynamic descriptions ⋮ Convergence of the quantum Navier-Stokes-Poisson equations to the incompressible Euler equations for general initial data

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