Related papers: The classical limit of dynamics for spaces quantiz…
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…
We discuss the classical and quantum mechanical evolution of systems described by a Hamiltonian that is a function of a solvable one, both classically and quantum mechanically. The case in which the solvable Hamiltonian corresponds to the…
Classical Hamiltonian system of a point moving on a sphere of fixed radius is shown to emerge from the constrained evolution of quantum spin. The constrained quantum evolution corresponds to an appropriate coarse-graining of the quantum…
Without wasting time and effort on philosophical justifications and implications, we write down the conditions for the Hamiltonian of a quantum system for rendering it mathematically equivalent to a deterministic system. These are the…
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…
Understanding how classical physics emerges from quantum mechanics remains a central problem in the foundations of physics. Here we derive a classical limit from finite-resolution measurements, modeled by continuous coarse-grained POVMs.…
We consider the classical limit of the quantum evolution, with some rough potential, of wave packets concentrated near singular trajectories of the underlying dynamics. We prove that under appropriate conditions, even in the case of BV…
The classical and quantum dynamics for an n-dimensional generalization of the kicked planar (n=1) rotator in an additional effective centrifugal potential. Therefore, typical phenomena like the diffusion in classical phase space are similar…
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.…
If there exists a classical, i.e. deterministic theory underlying quantum mechanics, an explanation must be found of the fact that the Hamiltonian, which is defined to be the operator that generates evolution in time, is bounded from below.…
Classical physics is reformulated as a constrained Hamiltonian system in the history phase space. Dynamics, i.e. the Euler-Lagrange equations, play the role of first-class constraints. This allows us to apply standard methods from the…
Constrained Hamiltonian description of the classical limit is utilized in order to derive consistent dynamical equations for hybrid quantum-classical systems. Starting with a compound quantum system in the Hamiltonian formulation conditions…
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…
On the basis of the non-commutative q-calculus, we investigate a q-deformation of the classical Poisson bracket in order to formulate a generalized q-deformed dynamics in the classical regime. The obtained q-deformed Poisson bracket appears…
A formalism is developed for describing approximate classical behaviour in finite (but possibly large) quantum systems. This is done in terms of a structure common to classical and quantum mechanics, viz. a Poisson space with a transition…
For a quantum observable $A_\hbar$ depending on a parameter $\hbar$ we define the notion ``$A_\hbar$ converges in the classical limit''. The limit is a function on phase space. Convergence is in norm in the sense that $A_\hbar\to0$ is…
The quantum description of time evolution in non-linear gravitational systems such as cosmological space-times is not well understood. We show, in the simplified setting of mini-superspace, that time evolution of this system can be obtained…
We investigate the classical limit of non-Hermitian quantum dynamics arising from a coherent state approximation, and show that the resulting classical phase space dynamics can be described by generalised "canonical" equations of motion,…
In this paper we consider generalization of classical and quantum mechanics that directly follows from the causality principle and topology of a system state space. In generalized mechanics, the Hamiltonian/Schrodinger equations remain the…
We study the dynamics of a "kicked" quantum system undergoing repeated measurements of momentum. A diffusive behavior is obtained for a large class of Hamiltonians, even when the dynamics of the classical counterpart is not chaotic. These…