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Constrained Hamiltonian description of the classical limit is utilized in order to derive consistent dynamical equations for hybrid quantum-classical systems. Starting with a compound quantum system in the Hamiltonian formulation, conditions for classical behavior are imposed on one of its subsystems and the corresponding hybrid dynamical equations are derived. The presented formalism suggests that the hybrid systems have properties that are not exhausted by those of quantum and classical systems. [ABSTRACT FROM AUTHOR]

A classical Hamiltonian system of a point moving on a sphere of fixed radius is shown to emerge from the constrained evolution of quantum spin. The constrained quantum evolution corresponds to an appropriate coarse graining of the quantum states into equivalence classes, and forces the equivalence classes to evolve as single units representing the classical states. The coarse-grained quantum spin with the constrained evolution in the limit of the large spin becomes indistinguishable from the classical system. [ABSTRACT FROM AUTHOR]

Two types of Hamiltonian hybrid quantum-classical theories are considered as potential models of the quantum measurement process. The two theories have the same Hamiltonian dynamics but differ in the association of states of the quantum system with states of the hybrid model. In the first type of association pure quantum states are modeled by pure states of the hybrid, while in the second type the pure quantum states are modeled by statistical mixtures of the hybrid pure states. It is shown that the second of the two theories describes correctly the quantum measurement while the first provides only an averaged description. [ABSTRACT FROM AUTHOR]

The possibility of state cloning is analyzed in two types of generalizations of quantum mechanics with nonlinear evolution. It is first shown that nonlinear Hamiltonian quantum mechanics does not admit cloning without the cloning machine. It is then demonstrated that the addition of the cloning machine, treated as a quantum or as a classical system, makes cloning possible by nonlinear Hamiltonian evolution. However, a special type of quantum-classical theory, known as the mean-field Hamiltonian hybrid mechanics, does not admit cloning by natural evolution. The latter represents an example of a theory where it appears to be possible to communicate between two quantum systems at superluminal speed, but at the same time it is impossible to clone quantum pure states. [ABSTRACT FROM AUTHOR]

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 [ABSTRACT FROM AUTHOR]