Related papers: Mathematics of the classical and the quantum
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),…
How much of the uncertainty in predicting measurement outcomes for non-commuting quantum observables is genuinely quantum mechanical? We provide a natural decomposition of the total entropic uncertainty of two non-commuting observables into…
This work explores the intersection of quantum mechanics and curved spacetime by employing the Wigner formalism to investigate quantum systems in the vicinity of black holes. Specifically, we study the quantum dynamics of a probe particle…
The correspondence principle states that classical mechanics emerges from quantum mechanics in the appropriate limits. However, beyond this heuristic rule, an information-theoretic perspective reveals that classical mechanics is a…
A unified conceptual foundation of classical and quantum physics is given, free of undefined terms. Ensembles are defined by extending the `probability via expectation' approach of Whittle to noncommuting quantities. This approach carries…
We describe both quantum particles and classical particles in terms of a classical statistical ensemble, characterized by a probability distribution in phase space. By use of a wave function in phase space both can be treated in the same…
The relationship between classical and quantum mechanics is usually understood via the limit $\hbar \rightarrow 0$. This is the underlying idea behind the quantization of classical objects. The apparent incompatibility of general relativity…
We introduce the concept of a "classical observable" as an operator with vanishingly small quantum fluctuations on a set of density matrices. It is shown how to construct them for a time evolved pure state. The study of classical…
Quantum dynamics can be regarded as a generalization of classical finite-state dynamics. This is a familiar viewpoint for workers in quantum computation, which encompasses classical computation as a special case. Here this viewpoint is…
Two categories of results regarding quantum measurements are derived in this work and applied to the problem of collapse. The first category is concerned with local and transient features of the entanglement between a macroscopic measuring…
A strong analog classical simulation of general quantum evolution is proposed, which serves as a novel scheme in quantum computation and simulation. The scheme employs the approach of geometric quantum mechanics and quantum informational…
This work presents a selective review of results concerning the mathematical interface between the classical and quantum aspects encountered in problems such as the nuclear mean-field dynamics or quantum Brownian motion. It is shown that…
We consider a set of macroscopic (classical) degrees of freedom coupled to an arbitrary many-particle Hamiltonian system, quantum or classical. These degrees of freedom can represent positions of objects in space, their angles, shape…
Based on an identified quantum relativity symmetry the contraction of which gives the Newtonian approximation of Galilean relativity, a quantum model of the physical space can be formulated with the Newtonian space seen in a way as the…
In the frames of classical mechanics the generalized Langevin equation is derived for an arbitrary mechanical subsystem coupled to the harmonic bath of a solid. A time-acting temperature operator is introduced for the quantum Klein-Kramers…
Mechanics is developed over a differentiable manifold as space of possible positions. Time is considered to fill a one--dimensional Riemannian manifold, so having the metric as lapse. Then the system is quantized with covariant instead of…
The dynamical equation of quantum mechanics are rewritten in form of dynamical equations for the measurable, positive marginal distribution of the shifted, rotated and squeezed quadrature introduced in the so called "symplectic tomography".…
The Schr\"odinger equation is shown to be equivalent to a constrained Liouville equation under the assumption that phase space is extended to Grassmann algebra valued variables. For onedimensional systems, the underlying Hamiltonian…
The imprints left by quantum mechanics in classical (Hamiltonian) mechanics are much more numerous than is usually believed. We show Using no physical hypotheses) that the Schroedinger equation for a nonrelativistic system of spinless…
A novel theory of hybrid quantum-classical systems is developed, utilizing the mathematical framework of constrained dynamical systems on the quantum-classical phase space. Both, the quantum and the classical descriptions of the respective…