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\centerline{\large \bf Hydrodynamic Closures for Quantum Kinetic Equations }



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\centerline{Christian Ringhofer}
\centerline{\it Arizona State University, Tempe, Arizona, USA}
\centerline{e-mail {\tt ringhofer@asu.edu}}



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The goal of quantum-hydrodynamic modeling is to derive quantum mechanical
corrections to classical fluid equations via moment closures of the
underlying quantum kinetic equation, i.e. the von Neumann equation
for the density matrix or the Wigner equation for the Wigner function.
These closures are obtained  via assumptions on the phase distribution of
the wave functions or from  thermodynamic principles. One of the main
problems with all these approaches is that the collision terms in the
quantum kinetic equation is usually not
very well understood. In this talk we give an overview over recent
developments in the derivation of quantum kinetic collision terms and the
resulting closure procedures.

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