Related papers: Quantum-Classical Interactions and Galois Type Ext…
A proposal of an algebraic model for the relation between a quantum environment and certain classical particle system is given. The quantum environment is described by a category of possible quantum states, the initial particle system is…
The concept of quantum commutativity with respect to an action or coaction of a given Hopf algebra is used for the algebraic description of a system of particles and their interaction with certain quantum field. Graded commutativity and…
We present three statistical descriptions for systems of classical particles and consider their extension to hybrid quantum-classical systems. The classical descriptions are ensembles on configuration space, ensembles on phase space, and a…
A consistent description of interactions between classical and quantum systems is relevant to quantum measurement theory, and to calculations in quantum chemistry and quantum gravity. A solution is offered here to this longstanding problem,…
We apply Hall and Reginatto's theory of interacting classical and quantum ensembles to harmonically coupled particles, with a view to understanding its experimental implications. This hybrid theory has no free parameters and makes…
We provide an overview of a canonical formalism that describes mixed quantum-classical systems in terms of statistical ensembles on configuration space, and discuss applications to measurement theory. It is shown that the formalism allows a…
An algebraic formalism for the study of interacting particle systems is developed. Particle processes are described in terms of the category theory. The problem for the unique description of these processes is discussed. Categories relevant…
In this work we provide a complete model of semiclassical theories by including back-reaction and correlation into the picture. We specially aim at the interaction between light and a two-level atom, and we also illustrate it via the…
We consider the links between consistent and approximate descriptions of the quantum-classical systems, i.e. systems are composed of two interacting subsystems, one of which behaves almost classically while the other requires a quantum…
The Hamiltonian conservative system of two interacting particles has been considered both in classical and quantum description. The quantum model has been realized using a symmetrized two-particle basis reordered in the unperturbed energy.…
The landscape of causal relations that can hold among a set of systems in quantum theory is richer than in classical physics. In particular, a pair of time-ordered systems can be related as cause and effect or as the effects of a common…
We present an algebraic framework for interacting extended quantum systems to study complex phenomena characterized by the coexistence and competition of different states of matter. We start by showing how to connect different…
We develop a so-called theory of ensembles in phase space and use it to investigate the construction of a quantum-classical hybrid theory. We use Galilei covariance and the Lie algebra of the Galilei group as a guide to constructing the…
A summary of a recently proposed description of quantum-classical hybrids is presented, which concerns quantum and classical degrees of freedom of a composite object that interact directly with each other. This is based on notions of…
In the framework of semiclassical theory the universal properties of quantum systems with classically chaotic dynamics can be accounted for through correlations between partner periodic orbits with small action differences. So far, however,…
We propose a new quantum approach for describing a system of $n$ interacting particles with variable mass connected by an unknown field with variable form ($n$-VMVF systems). Instead of assuming any particular nature for variation of the…
The relation that exists in quantum mechanics among action variables, angle variables and the phases of quantum states is clarified, by referring to the system of a generalized oscillator. As a by-product, quantum-mechanical meaning of the…
We review canonical experiments on systems that have pushed the boundary between the quantum and classical worlds towards much larger scales, and discuss their unique features that enable quantum coherence to survive. Because the types of…
An exact correspondence is established between a $N$-body classical interacting system and a $N-1$-body quantum system with respect to the partition function. The resulting quantum-potential is a $N-1$-body one. Inversely the Kelbg…
In the study of open quantum systems modeled by a unitary evolution of a bipartite Hilbert space, we address the question of which parts of the environment can be said to have a "classical action" on the system, in the sense of acting as a…