Path integral centroid molecular dynamics method for Bose and Fermi statistics: formalism and simulation

A method is proposed for path integral centroid molecular dynamics (CMD) extended to Bose/Fermi statistics. It is based on the `pseudo-Boltzmannʹ canonical partition function of quantum statistical mechanics. An extended technique of path integral molecular dynamics (PIMD) is further presented for the calculation of thermodynamic properties and centroid mean force of Bose/Fermi systems. Bosonic PIMD and CMD simulations have been performed for 4He and the ideal Bose gas, respectively. The remnant of λ transition is observed for 4He, while Bose statistics causes a decay of the centroid velocity autocorrelation function of the ideal Bose gas in a nanosecond scale.