An approach for generating trajectory-based dynamics which conserves the canonical distribution in the phase space formulation of quantum mechanics. I. Theories

We have reformulated and generalized our recent work [J. Liu and W. H. Miller, J. Chem. Phys. 126, 234110 (2007)] into an approach for generating a family of trajectory-based dynamics methods in the phase space formulation of quantum mechanics. The approach (equilibrium Liouville dynamics) is in the spirit of Liouville's theorem in classical mechanics. The trajectory-based dynamics is able to conserve the quantum canonical distribution for the thermal equilibrium system and approaches classical dynamics in the classical (h -> 0), high temperature (beta -> 0), and harmonic limits. Equilibrium Liouville dynamics provides the framework for the development of novel theoretical/computational tools for studying quantum dynamical effects in large/complex molecular systems. (C) 2011 American Institute of Physics. [doi:10.1063/1.3555273]