Related papers: A simple mathematical formulation of the correspon…
In a companion paper (hereafter referred to as Paper I), we have presented an attempt to derive the finite-dimensional abstract quantum formalism from a set of physically comprehensible assumptions. In this paper, we formulate a…
We present a detailed analysis of the scattering of charged particles by the magnetic field of a long solenoid of constant magnetic flux and finite radius. We study the relativistic and non-relativistic quantum and classical scenarios. The…
We propose to study the $L^2$-norm distance between classical and quantum phase space distributions, where for the latter we choose the Wigner function, as a global phase space indicator of quantum-classical correspondence. For example,…
Probability waves in the configuration space are associated with coherent solutions of the classical Liouville or Fokker-Planck equations. Distributions localized in the momentum space provide action waves, specified by the probability…
In the limit of large quantum excitations, the classical and quantum probability distributions for a Schr\"odinger equation can be compared by using the corresponding WKBJ solutions whose rapid oscillations are averaged. This result is…
The correspondence principle is investigated in the framework of deterministic predictions for individual systems. Exact analytical results are obtained for the quantum and the Liouvillian dynamics of a nonlinear oscillator coupled to a…
We consider a simple quantum system subjected to a classical random force. Under certain conditions it is shown that the noise-averaged Wigner function of the system follows an integro-differential stochastic Liouville equation. In the…
In quantum physics, the density operator completely describes the state. Instead, in classical physics the mean value of every physical quantity is evaluated by means of a probability distribution. We study the possibility to describe pure…
The famous Nils Bohr's quantum-classical correspondence principle states that the classical mechanics is a limiting case of the more general quantum mechanics. This implies that ``under certain conditions" quantum laws of motion become…
We develop a consistent perturbation theory in quantum fluctuations around the classical evolution of a system of interacting bosons. The zero order approximation gives the classical Gross-Pitaevskii equations. In the next order we recover…
In a companion paper (hereafter referred to as Paper I), we have presented an attempt to derive the finite-dimensional abstract quantum formalism within the framework of information geometry. In this paper, we formulate a correspondence…
A one-dimensional model of classical diffusion in a random force field with a weak concentration $\rho$ of absorbers is studied. The force field is taken as a Gaussian white noise with $\mean{\phi(x)}=0$ and $\mean{\phi(x)\phi(x')}=g…
Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by…
We present evidence that decoherence can produce a smooth quantum-to-classical transition in nonlinear dynamical systems. High-resolution tracking of quantum and classical evolutions reveals differences in expectation values of…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitudes, Born rule,…
We introduce a density tensor hierarchy for open system dynamics, that recovers information about fluctuations lost in passing to the reduced density matrix. For the case of fluctuations arising from a classical probability distribution,…
The investigation of quantum-classical correspondence may lead to gain a deeper understanding of the classical limit of quantum theory. We develop a quantum formalism on the basis of a linear-invariant theorem, which gives an exact…
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…
We study the interrelations between the classical (Frobenius-Perron) and the quantum (Husimi) propagator for phase-space (quasi-)probability densities in a Hamiltonian system displaying a mix of regular and chaotic behavior. We focus on…
How should we model an observer within quantum mechanics or quantum field theory? How can classical physics emerge from a quantum model, and why should classical probability be useful? How can we model a selective measurement entirely…