On the derivation and mathematical analysis of some quantum–mechanical models accounting for Fokker–Planck type dissipation: Phase space, Schrödinger and hydrodynamic descriptions

• Published in: Nanoscale systems mathematical modeling, theory and applications Vol. 2; pp. 49 - 80
• Main Authors: López, José Luis, Montejo–Gámez, Jesús
• Format: Journal Article
• Language: English
• Published: Versita 27.02.2013
• Subjects: 02.30.Jr; 03.65.Db; 03.65.Yz; 35A07; 35G30; 35Q55; 47.10.A; 47.10.ad; 47.37.+q; 76Y05; 78M05; 81Q05; 81S30; dissipative quantum mechanics; Doebner-Goldin equations; logarithmic nonlinearity; Madelung decomposition; nonlinear Gauge transformations; nonlinear Schrödinger equations; Open quantum system; osmotic momentum; quantum Navier-Stokes equations; quantum viscous hydrodynamic equations; Wigner-Fokker-Planck equation
• ISSN: 2299-3290; 2299-3290
• DOI: 10.2478/nsmmt-2013-0004

This paper is intended to provide the reader with a review of the authors’ latest results dealing with the modeling of quantum dissipation/diffusion effects at the level of Schrödinger systems, in connection with the corresponding phase space and fluid formulations of such kind of phenomena, especially in what concerns the role of the Fokker–Planck mechanism in the description of open quantum systems and the macroscopic dynamics associated with some viscous hydrodynamic models of Euler and Navier–Stokes type.