Statistical Properties of Fermionic Molecular Dynamics.pdf

Statistical Prop erties of Fermionic Molecular Dynamics J Schnack and H Feldmeier Gesel lschaft fur Schwerionenforschung mbH Postfach D Darmstadt Technische Hochschule Darmstadt Abstract Statistical prop erties of Fermionic Molecular Dynamics are studied It is shown that although the centroids of the singleparticle wavepackets follow classical tra jectories in the case of a harmonic oscillator p otential the equilibrium prop erties of the system are the quantum mechanical ones A system of weakly interacting fermions as well as of distinguishable particles is found to b e ergo dic and the time averaged o ccupation probabilities approach the quantum canonical ones of Fermi Dirac and Boltzmann statistics resp ectively Intro duction and summary Molecular dynamic mo dels are exp ected to describ e multifragmentation of nu clei seen in heavyion collisions These reactions show large uctuations for example in the mass distribution which are b eyond an ensembleaveraged meaneld treatment In this context it is imp ortant to understand the statis tical prop erties of molecular dynamic mo dels esp ecially at low temp eratures There are two asp ects of this One concerns the thermo static prop erties of a molecular dynamic mo del where the attribute thermostatic refers to the prop erties of the static canonical statistical op erator which are contained in the H partition function Z T Trexp f T g Once the partition function is calculated within a given mo del its thermostatic prop erties can b e deduced by standard metho ds like partial derivatives of ln Z T with resp ect to tem p erature T or other parameters contained in the Hamilton op erator H An