相关论文: Quantum Mechanics as an Approximation to Classical…

This paper addresses the question why quantum mechanics is formulated in a unitary Hilbert space, i.e. in a manifestly complex setting. Investigating the linear dynamics of real quantum theory in a finite-dimensional Euclidean Hilbert space…

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".…

Based on a number of experimentally verified physical observations, it is argued that the standard principles of quantum mechanics should be applied to the Universe as a whole. Thus, a paradigm is proposed in which the entire Universe is…

We show that the classical mechanics of an algebraic model are implied by its quantizations. An algebraic model is defined, and the corresponding classical and quantum realizations are given in terms of a spectrum generating algebra.…

We have previously presented a version of the Weak Equivalence Principle for a quantum particle as an exact analog of the classical case, based on the Heisenberg picture analysis of free particle motion. Here, we take that to a full…

In categorical quantum mechanics, classical structures characterize the classical interfaces of quantum resources on one hand, while on the other hand giving rise to some quantum phenomena. In the standard Hilbert space model of quantum…

We review here the quantum mechanics of some noncommutative theories in which no state saturates simultaneously all the non trivial Heisenberg uncertainty relations. We show how the difference of structure between the Poisson brackets and…

Classical transport equations with probabilistic initial conditions can be viewed as quantum systems. In a discrete version they are probabilistic automata. The time-local probabilistic information is encoded in a classical wave function.…

Using a group theoretical approach we derive an equation of motion for a mixed quantum-classical system. The quantum-classical bracket entering the equation preserves the Lie algebra structure of quantum and classical mechanics: The bracket…

In loop quantum cosmology the quantum dynamics is well understood. We approximate the full quantum dynamics in the infinite dimensional Hilbert space by projecting it on a finite dimensional submanifold thereof, spanned by suitably chosen…

We consider a semi-classical approximation to the dynamics of a point particle in a noncommutative space. In this approximation, the noncommutativity of space coordinates is described by a Poisson bracket. For linear Poisson brackets, the…

Wigner's quasi-probability distribution function in phase-space is a special (Weyl) representation of the density matrix. It has been useful in describing quantum transport in quantum optics; nuclear physics; decoherence (eg, quantum…

Observables in a quantum system, represented by a Hilbert space, are given by the orthogonal bases of the aforementioned Hilbert space. Categorical Quantum Mechanics provides further abstraction of such observables, allowing for a…

The application of a classical approach to various quantum problems - the secular perturbation approach to quantization of a hydrogen atom in external fields and a helium atom, the adiabatic switching method for calculation of a…

The generalized h-dependent operator algebra is defined ($0\leq h \leq h_o$). For h= h_o it becomes equivalent to the quantum mechanical algebra of observables and for h=0 it is equivalent to the classical one. We show this by proposing how…

We consider a 3-parametric linear deformation of the Poisson brackets in classical mechanics. This deformation can be thought of as the classical limit of dynamics in so-called "quantized spaces". Our main result is a description of the…

Quantum mechanics is widely regarded as a complete theory, yet we argue it is a tractable projection of a deeper, computationally-inaccessible classical variational structure. By analyzing the coupled partial differential equations of the…

Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the…

In spite of its popularity, it has not been possible to vindicate the conventional wisdom that classical mechanics is a limiting case of quantum mechanics. The purpose of the present paper is to offer an alternative point of view in which…

A generalization of classical mechanics is obtained from a complex parametrization of the phase space. The formalism supports complex Hamiltonian functions describing non-conservative classical mechanical systems. A quantization scheme that…