Related papers: The Quantum-Classical Transition: The Fate of the …
We describe quantum and classical Hamiltonian dynamics in a common Hilbert space framework, that allows the treatment of mixed quantum-classical systems. The analysis of some examples illustrates the possibility of entanglement between…
We consider the dynamics of interacting quantum and classical systems in the Heisenberg representation. Unlike the usual construction in standard quantum mechanics, mixed quantum-classical systems involve the interplay of unitary operators…
What does it take for real-deterministic c-valued (i.e., classical, commuting) variables to comply with the Heisenberg uncertainty principle? Here, we construct a class of real-deterministic c-valued variables out of the weak values…
Classical macroscopic space-time is pictured in terms of Rydberg states of an underlying discritzed `atomic' quantum geometry at Planck scales. While quantum geometry on such scales involves several very short lived transitions changing…
Semiclassical methods have been applied very successfully to describe the nontrivial transition from the quantum to the classical regime in $\textit{single}$-particle or at least $\textit{few}$-particle systems. Challenges on the way to an…
The usual Heisenberg uncertainty relation for position and momentum may be replaced by an exact equality, for suitably chosen measures of position and momentum uncertainty. This "exact" uncertainty relation is valid for_all_ pure states,…
We present a quantitative analysis of the reversibility properties of classically chaotic quantum motion. We analyze the connection between reversibility and the rate at which a quantum state acquires a more and more complicated structure…
This is a self-contained introduction to quantum Riemannian geometry based on quantum groups as frame groups, and its proposed role in quantum gravity. Much of the article is about the generalisation of classical Riemannian geometry that…
We formulate a general principle that supplants a Boolean \sigma-algebra of intrinsic properties of a classical system by a \sigma-complex (a union of \sigma-algebras) of extrinsic properties of a quantum system that are elicited by…
The aim of this paper is to review the classical limit of Quantum Mechanics and to precise the well known threat of chaos (and fundamental graininess)to the correspondence principle. We will introduce a formalism for this classical limit…
Heisenberg's uncertainty principle is often cited as an example of a "purely quantum" relation with no analogue in the classical limit where $\hbar \to 0$. However, this formulation of the classical limit is problematic for many reasons,…
To solve the quantum-mechanical problem the procedure of mapping onto linear space $W$ of generators of the (sub)group violated by given classical trajectory is formulated. The formalism is illustrated by the plane H-atom model. The problem…
Quantum information and computation may serve as a source of useful axioms and ideas for the quantum logic/quantum structures project of characterizing and classifying types of physical theories, including quantum mechanics and classical…
Standard quantum mechanics unquestionably violates the separability principle that classical physics (be it point-like analytic, statistical, or field-theoretic) accustomed us to consider as valid. In this paper, quantum nonseparability is…
We propose a mathematical model of quantum spacetime as an infinite-dimensional manifold locally homeomorphic to an appropriate Schwartz space. This extends and unifies both the standard function space construction of quantum mechanics and…
Different approaches are compared to formulation of quantum mechanics of a particle on the curved spaces. At first, the canonical, quasi-classical and path integration formalisms are considered for quantization of geodesic motion on the…
The mechanism of the transition of a dynamical system from quantum to classical mechanics is one of the remaining challenges of quantum theory. Currently, it is considered to occur via decoherence caused by entanglement and/or stochastic…
Starting with the generally well accepted opinion that quantizing an arbitrary Hamiltonian system involves picking out some additional structure on the classical phase space (the {\sl shadow} of quantum mechanics in the classical theory),…
Quantum and classical physical states are represented in a unified way when they are described by symplectic tomography. Therefore this representation allows us to study directly the necessary conditions for a classical universe to emerge…
15 years ago Dmitry Diakonov wrote the paper "Towards lattice-regularized Quantum Gravity", arXiv:1109.0091. In his approach, gravity with metric and tetrads arise from pre-geometric quantum fields leading to unusual dimensions of physical…