Statistical ensembles in Hamiltonian formulation of hybrid quantum-classical systems

Abstract

General statistical ensembles in the Hamiltonian formulation of hybrid quantum-classical systems are analyzed. It is argued that arbitrary probability densities on the hybrid phase space must be considered as the class of possible physically distinguishable statistical ensembles of hybrid systems. Nevertheless, statistical operators associated with the hybrid system and with the quantum subsystem can be consistently defined. Dynamical equations for the statistical operators representing the mixed states of the hybrid system and its quantum subsystem are derived and analyzed. In particular, these equations irreducibly depend on the total probability density on the hybrid phase space.Comment: This is the published version of the paper with an added note with an observation made after the paper was accepted. The main conclusions are as in the published version but the final formula is considerably simplife