A derivation of the isothermal quantum hydrodynamic equations using entropy minimization

Ansgar Jünger; Daniel Matthes

doi:10.1002/zamm.200510232

A derivation of the isothermal quantum hydrodynamic equations using entropy minimization

Ansgar Jünger, Daniel Matthes

Johannes Gutenberg University

Research output: Contribution to journal › Article › peer-review

35 Scopus citations

Abstract

Isothermal quantum hydrodynamic equations of order O(ℏ²) 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(ℏ²) which involves the vorticity. If the initial vorticity is of order O(ℏ), the standard model is obtained up to order O(ℏ⁴). The derivation is based on a careful expansion of the quantum equilibrium obtained from the entropy minimization in powers of ℏ².

Original language	English
Pages (from-to)	806-814
Number of pages	9
Journal	ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
Volume	85
Issue number	11
DOIs	https://doi.org/10.1002/zamm.200510232
State	Published - Nov 2005
Externally published	Yes

Keywords

Moment method
Quantum entropy
Quantum hydrodynamics
Relaxation-time Wigner equation

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10.1002/zamm.200510232

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AB - Isothermal quantum hydrodynamic equations of order O(ℏ2) 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(ℏ2) which involves the vorticity. If the initial vorticity is of order O(ℏ), the standard model is obtained up to order O(ℏ4). The derivation is based on a careful expansion of the quantum equilibrium obtained from the entropy minimization in powers of ℏ2.

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KW - Quantum entropy

KW - Quantum hydrodynamics

KW - Relaxation-time Wigner equation

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A derivation of the isothermal quantum hydrodynamic equations using entropy minimization

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Keywords

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