A semiclassical approach to the dynamics of many-body Bose/Fermi systems by the path integral centroid molecular dynamics

We present a formalism of the path integral centroid molecular dynamics (CM D) extended to Bose and Fermi statistics as a semiclassical approach to exp lore the dynamics of quantum many-body systems. The validity of the method is examined in relation to the time correlation functions. The presently pr oposed scheme, refined from our previous derivation [Chem. Phys. Lett. 307, 187 (1999)], is aimed at the calculations of not the exact quantum-mechani cal dynamics but the semiclassical dynamics under certain approximations. T he formalism is based on the projection operator with which the Bose/Fermi system is mapped onto a particular type of pseudo-Boltzmann system. In the pseudo-Boltzmann system the correlation due to the Bose/Fermi statistics is introduced via an extra pseudopotential called the permutation potential a nd its relevant operator. Using the present semiclassical formalism, the ti me correlation function of centroid position, which is evaluated from the C MD trajectories in the pseudo-Boltzmann system, is an approximation to the Kubo canonical correlation function of position operator of the exact quant um-statistical system composed of bosons or fermions. There is no such appa rent relation between the momentum operator and the corresponding momentum centroid. (C) 2001 American Institute of Physics.