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Physica A Statistical Mechanics and its Applications

Generalized nonlinear Doebner-Goldin Schrödinger equation and the relaxation of quantum systems

V. V. Dodonov, Salomon Sylvain Mizrahi

Published Apr 1, 1995• 8 citations
Publisher
DOI
10.1016/0378-4371(94)00239-p

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The aim of this paper is to derive the quantum hydrodynamic system associated with the most general class of nonlinear Schrödinger equations accounting for Fokker--Planck type diffusion of the probability density, called of Doebner--Goldin. This 'Doebner--Goldin hydrodynamic system' is shown to be reduced in most cases to a simpler one of quantum Euler type by means of the introduction of a nonlinear gauge transformation that changes the fluid mean velocity into a new effective velocity corrected by an osmotic contribution. Finally, we also discuss some particular situations of especial interest and compare the structure of the resulting fluid systems with that of the viscous quantum hydrodynamic and the quantum Navier--Stokes equations stemming from maximization of the quantum entropy for Wigner--BGK models.