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

• Autorzy: José Luis López , Jesús Montejo–Gámez
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Open quantum system; Wigner-Fokker-Planck equation; Doebner-Goldin equations; nonlinear Schrödinger equations; quantum viscous hydrodynamic equations; quantum Navier-Stokes equations; dissipative quantum mechanics; logarithmic nonlinearity; nonlinear Gauge transformations; Madelung decomposition; osmotic momentum

Kategorie tematyczne

• 35Q55: NLS-like equations (nonlinear Schr\"odinger)
• 78M05: Method of moments
• 81Q05: Closed and approximate solutions to the Schr\"odinger, Dirac, Klein-Gordon and other equations of quantum mechanics
• 35G30: Boundary value problems for nonlinear higher-order equations
• 81S30: Phase-space methods including Wigner distributions, etc.
• 76Y05: Quantum hydrodynamics and relativistic hydrodynamics

• 03.65.Yz: Decoherence; open systems; quantum statistical methods(see also 03.67.Pp in quantum information; for decoherence in Bose-Einstein condensates, see 03.75.Gg)
• 47.37.+q: Hydrodynamic aspects of superfluidity; quantum fluids(for transport and hydrodynamics of normal and superfluid phase of 4He, see 67.25.bf, and 67.25.dg respectively; for transport and hydrodynamics of normal and superfluid phase of 3He, see 67.30.eh, and 67.30.hb respectively)
• 03.65.Db: Functional analytical methods
• 02.30.Jr: Partial differential equations
• 47.10.ad: Navier-Stokes equations
• 47.10.A-: Mathematical formulations

• Wydawca: De Gruyter Open
• Czasopismo: Nanoscale Systems: Mathematical Modeling, Theory and Applications
• Rocznik: 2013
• Tom: 2
• Strony: 49-80

Daty

otrzymano

2012-11-14

poprawiono

2013-01-31

zaakceptowano

2013-02-04

online

2013-02-27

Twórcy

autor

José Luis López

• Departamento de Matemática Aplicada,
  Facultad de Ciencias, Universidad de Granada,
  18071 Granada, Spain

autor

Jesús Montejo–Gámez

• Departamento de Matemática Aplicada,
  Facultad de Ciencias, Universidad de Granada,
  18071 Granada, Spain

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Identyfikatory

DOI

10.2478/nsmmt-2013-0004