Feynman path centroid dynamics for Fermi–Dirac statistics

Abstract

In this communication the centroid molecular dynamics (CMD) method is tested for systems of fermions using a modified version of the expression for the fermion Feynman path centroid density derived in a recent publication [J. Chem. Phys. 110, 3647 (1999)]. The method is applied to a model system consisting of two noninteracting fermions in an anharmonic potential well and the position autocorrelation function is computed. The exact fermion position autocorrelation function exhibits a longer period of oscillation when compared to the bosonic case. This shift is due to the anharmonic nature of the given potential function where the level spacing decreases with the increase of energy. The CMD results agree very well with the exact quantum mechanical results for this example. This indicates, along with the previous results on a boson system, that quantum statistics can in principle be incorporated into the CMD method without any degradation of the accuracy of the approximation.