Titlebook: Ensembles on Configuration Space; Classical, Quantum, Michael J. W. Hall,Marcel Reginatto Book 2016 Springer International Publishing Swit

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Radiation

Concrete

Interaction, Locality and Measurement formalism of ensembles on configuration space, this description requires a probability distribution .(.,?.) defined over the joint configuration space, the corresponding conjugate quantity .(.,?.), and an ensemble Hamiltonian .. Once a composite system is defined, it becomes necessary to introduce

一再煩擾

Thermodynamics and Mixtures on Configuration Spacespace ensemble . with probability ., then it may be said to correspond to the mixture .. Mixtures for classical and quantum systems are shown to be equivalent to phase space densities and density operators, respectively, and obey corresponding classical and quantum Liouville equations. We also gener

LEER

Quantization of Classical Ensembles via an Exact Uncertainty Principlen of the momentum of a quantum state into classical and nonclassical components and choosing suitable measures of position and momentum uncertainty. The exact uncertainty relation obtained in this way is sufficiently strong to provide the basis for moving from classical mechanics to quantum mechanic

Factual

The Geometry of Ensembles on Configuration Spacehich derives from the natural geometry associated with a space of probabilities, and a symplectic structure, which derives from the symplectic geometry associated with a Hamiltonian description of motion. We show that these two geometrical structures give rise to a K?hler geometry. We first consider

Factual

Obloquy

Obscure

Consistency of Hybrid Quantum-Classical Ensemblesapter, we consider such hybrid ensembles and focus on consistency requirements for models of quantum-classical interactions. We show how the configuration ensemble approach is able to satisfy desirable properties such as a Lie algebra of observables and Ehrenfest relations, while evading no-go theor

束縛

Ensembles of Classical Gravitational Fieldsobi formulation of general relativity. After a brief review of the Einstein–Hamilton–Jacobi equation in the metric representation, we introduce the additional mathematical structure that is needed to formulate the theory of configuration space ensembles; i.e., a measure over the space of metrics and