On the Feynman path centroid density for Bose-Einstein and Fermi-Dirac statistics

Expressions are derived for the Feynman path centroid density of systems of identical particles, namely, Bosons and Fermions. The resulting expression s are applied to a system of two independent particles in a quartic oscilla tor and the corresponding centroid densities are computed, plotted and comp ared to the distinguishable particle case. In regions where the particle ce ntroids are close to each other, the Boson centroid density displays an enh anced amplitude in comparison to the distinguishable case. This behavior is attributed to the attractive correlations in Boson systems. The Fermion ce ntroid density, however, can have the peculiar property of being negative i n those regions where the particle centroids are in close proximity. This f eature is related to the Pauli exclusion principle. This property of the Fe rmion centroid density rules out its strict interpretation as a probability distribution. Equilibrium properties such as the canonical partition funct ion and the average position were accurately computed using both densities. The Boson density was also used to compute the position autocorrelation fu nction using the Centroid Molecular Dynamics method and the results are in excellent agreement with those of an exact quantum calculation. (C) 1999 Am erican Institute of Physics. [S0021-9606(99)00508-5].