Premium
A derivation of the isothermal quantum hydrodynamic equations using entropy minimization
Author(s) -
Jüngel A.,
Matthes D.
Publication year - 2005
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200510232
Subject(s) - minification , quantum , isothermal process , vorticity , physics , entropy (arrow of time) , mathematical physics , mathematics , statistical physics , quantum mechanics , thermodynamics , mathematical optimization , vortex
AbstractDedicated to Prof. Herbert Gajewski in occasion of his 65th birthday Isothermal quantum hydrodynamic equations of order ( $\hbar$ 2 ) using the quantum entropy minimization method recently developed by Degond and Ringhofer are derived. The equations have the form of the usual quantum hydrodynamic model including a correction term of order ( $\hbar$ 2 which involves the vorticity. If the initial vorticity is of order ( $\hbar$ 4 , the standard model is obtained up to order . The derivation is based on a careful expansion of the quantum equilibrium obtained from the entropy minimization in powers of $\hbar$ 2 .