相关论文: On Koopman-von Neumann Waves
Students encounter harmonic-oscillator models in many aspects of basic physics, within widely-varying theoretical contexts. Here we highlight the interconnections and varying points of view. We start with the classical mechanics of masses…
We consider the quantum mechanical equivalence of the Seiberg-Witten map in the context of the Weyl-Wigner-Groenewold-Moyal phase-space formalism in order to construct a quantum mechanics over noncommutative Heisenberg algebras. The…
A recent formalism capturing the classical-quantum coupling in a Hamiltonian theory for probabilistic classical mechanics has been proposed: the Koopman-van Hove formulation. The aims of this report are twofolds. First, we rigourously…
Finding a physically consistent approach to modelling interactions between classical and quantum systems is a highly nontrivial task. While many proposals based on various mathematical formalisms have been made, most of these efforts run…
We propose a simulation strategy which uses a classical device of linearly coupled chain of springs to simulate quantum dynamics, in particular the quantum walks. Through this strategy, we obtain the quantum wave function from classical…
Bohmian mechanics, a hydrodynamic formulation of the quantum theory, constitutes a useful tool to understand the role of the phase as the mechanism responsible for the dynamical evolution displayed by quantum systems. This role is analyzed…
In spite of all {\bf no-go} theorems (e.g., von Neumann, Kochen and Specker,..., Bell,...) we constructed a realist basis of quantum mechanics. In our model both classical and quantum spaces b are rough images of the fundamental {\bf…
Using quantum-classical analogies, we find that dynamical pictures of quantum mechanics have precise counterparts in classical mechanics. In particular, the Eulerian and Lagrangian descriptions of fluid dynamics in classical mechanics are…
We constructed a Hilbert space representation of a contextual Kolmogorov model. This representation is based on two fundamental observables -- in the standard quantum model these are position and momentum observables. This representation…
The Koopman--von Neumann equation describes the evolution of a complex-valued wavefunction corresponding to the probability distribution given by an associated classical Liouville equation. Typically, it is defined on the whole Euclidean…
In our previous papers we were interested in making a reconstruction of quantum mechanics according to classical mechanics. In this paper we suspend this program for a while and turn our attention to a theme in the frontier of quantum…
It is well known that Niels Bohr insisted on the necessity of classical concepts in the account of quantum phenomena. But there is little consensus concerning his reasons, and what he exactly meant by this. In this paper, I re-examine…
We provide a Hilbert space approach to quantum mechanics where space and time are treated on an equal footing. Our approach replaces the standard dependence on an external classical time parameter with a spacetime-symmetric algebraic…
Cirelli, Mani\`{a} and Pizzocchero generalized quantum mechanics by K\"{a}hler geometry. Furthermore they proved that any unital C$^{*}$-algebra is represented as a function algebra on the set of pure states with a noncommutative…
The spread of the wave-function, or quantum uncertainty, is a key notion in quantum mechanics. At leading order, it is characterized by the quadratic moments of the position and momentum operators. These evolve and fluctuate independently…
A local interpretation of quantum mechanics is presented. Its main ingredients are: first, a label attached to one of the virtual paths in the path integral formalism, determining the output for measurement of position or momentum; second,…
A correspondence is established between measure-preserving, ergodic dynamics of a classical harmonic oscillator and a quantum mechanical gauge theory on two-dimensional Minkowski space. This correspondence is realized through an isometric…
In the first part of this paper the general perspective of history quantum theories is reviewed. History quantum theories provide a conceptual and mathematical framework for formulating quantum theories without a globally defined…
This work gives value to the importance of Hilbert-Schmidt operators in the formulation of a noncommutative quantum theory. A system of charged particle in a constant magnetic field is investigated in this framework.
The classical limit $\hbar$->0 of quantum mechanics is known to be delicate, in particular there seems to be no simple derivation of the classical Hamilton equation, starting from the Schr\"odinger equation. In this paper I elaborate on an…