Quantum Partitioning Methods for Few-Atom and Many-Atom Dynamics

The subject of this contribution is how projection operators can be constructed to treat a variety of time-dependent phenomena involving interacting molecules, and to treat the dissipative dynamics of a localized subsystem in a large environment. It develops partitioning methods in a functional space of wavefunctions introduced to construct molecular effective potentials and long-lived states from distortion, adiabatic, and fast motion states. It also gives a treatment starting from the statistical density operator, for partitioning in a many-atom system undergoing dissipative dynamics, and shows how to construct contracted density operators with selected total system states, or reduced density operators for localized phenomena in a primary region. The presentation displays related mathematical procedures useful for partitioning of both wavefunctions and density operators and for derivation of their equations of motion.