2 Wigner Function Quantum Molecular Dynamics

Classical molecular dynamics (MD) is a well established and powerful tool in various fields of science, e.g. chemistry, plasma physics, cluster physics and condensed matter physics. Objects of investigation are few-body systems and many-body systems as well. The broadness and level of sophistication of this technique is documented in many monographs and reviews, see for example [1, 2]. Here we discuss the extension of MD to quantum systems (QMD). There have been many attempts in this direction which differ from each other, depending on the type of system under consideration. One variety of QMD has been developed for condensed matter systems. This approach is reviewed e.g. in [3] and will not be discussed here. In this contribution we deal with unbound electrons as they occur in gases, fluids or plasmas. Here, a quite successful strategy is to replace classical point particles by wave packets [3, 4, 5, 6]. This method, however, struggles with problems related to the dispersion of such a wave packet and difficulties to properly describe strong electron-ion interaction and bound-state formation. We try to avoid these restrictions by an alternative approach: We start the discussion of quantum dynamics by a general consideration of quantum distribution functions.