A derivation of the isothermal quantum hydrodynamic equations using entropy minimization

作者：Jungel A^*; Matthes D

来源：Zeitschrift fur Angewandte Mathematik und Mechanik, 2005, 85(11): 806-814.

DOI：10.1002/zamm.200510232

• quantum hydrodynamics
• relaxation-time Wigner equation
• quantum entropy
• moment method

Isothermal quantum hydrodynamic equations of order O (h(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 O (h(2)) which involves the vorticity. If the initial vorticity is of order O (h), the standard model is obtained up to order O (h(4)). The derivation is based on a careful expansion of the quantum equilibrium obtained from the entropy minimization in powers of h(2).

• 出版日期2005-11