Related papers: Continuous Transitions Between Quantum and Classic…
Classical equations of motion that are first-order in time and conserve energy can only be quantized after their variables have been transformed to canonical ones, i.e., variables in which the energy is the system's Hamiltonian. The…
"Physical theories of fundamental significance tend to be gauge theories. These are theories in which the physical system being dealt with is described by more variables than there are physically independent degree of freedom. The…
We study the difference between quantum and classical behavior in a pair of nonidentical cavities with second-harmonic generation. In the classical limit, each cavity has a limit-cycle solution, in which the photon number oscillates…
The quantum mechanics of superconducting circuits is derived by starting from a classical Hamiltonian dynamical system describing a dissipationless circuit, usually made of capacitive and inductive elements. However, standard approaches to…
In their simplest formulations, classical dynamics is the study of Hamiltonian flows and quantum mechanics that of propagators. Both are linked, and emerge from the datum of a single classical concept, the Hamiltonian function. We study and…
A detailed study is made of the space-time transformation properties of intercharge forces and the associated electric and magnetic force fields, both in classical electrodynamics and in a recently developed relativistic classical…
In order to extend the limits of classical theory application in the microworld some weak generalization of Maxwell electrodynamics is suggested. It is shown that slightly generalized classical Maxwell electrodynamics can describe the…
If we admit that quantum mechanics (QM) is universal theory, then QM should contain also some description of classical mechanical systems. The presented text contains description of two different ways how the mathematical description of…
We consider the semiclassical equations of motion of a particle when both an external electromagnetic field and the Berry gauge field in the momentum space are present. It is shown that these equations are Hamiltonian and relations between…
We consider the two main theorems in the derivation of the Quantum Hamilton--Jacobi Equation from the Equivalence Postulate (EP) of quantum mechanics. The first one concerns a basic cocycle condition, which holds in any dimension with…
In this paper, I argue that light is a continuous classical electromagnetic wave, while the observed so-called quantum nature of the interaction of light with matter is connected to the discrete (atomic) structure of matter and to the…
It is demonstrated how all the mechanical equations of classical electrodynamics (CEM) may be derived from only Coulomb's inverse square force law, special relativity and Hamilton's Principle. The instantaneous nature of the Coulomb force…
A gauge-invariant Wigner quasi-distribution function for charged particles in classical electromagnetic fields is derived in a rigorous way. Its relation to the axial gauge is discussed, as well as the relation between the kinetic and…
Makowski and Konkel [Phys. Rev. A 58, 4975 (1998)] have obtained certain classes of potentials which lead to identical classical and quantum Hamilton-Jacobi equations. We obtain the most general form of these potential.
This paper offers an informal instructive introduction to some of the main notions of geometric continuum mechanics for the case of smooth fields. We use a metric invariant stress theory of continuum mechanics to formulate a simple…
An eigenvalue equation representing symmetric (dual) quantum equation is introduced. The particle is described by two scalar wavefunctions, and two vector wavefunctions. The eigenfunction is found to satisfy the quantum Telegraph equation…
We review the modern classical electrodynamics problems and present the related main fundamental principles characterizing the electrodynamical vacuum-field structure. We analyze the models of the vacuum field medium and charged point…
While ultimately they are described by quantum mechanics, macroscopic mechanical systems are nevertheless observed to follow the trajectories predicted by classical mechanics. Hence, in the regime defining macroscopic physics, the…
The inadequacy of Li\'{e}nard-Wiechert potentials is demonstrated as one of the examples related to the inconsistency of the conventional classical electrodynamics. The insufficiency of the Faraday-Maxwell concept to describe the whole…
We study the motion of a particle in a particular magnetic field configuration both classically and quantum mechanically. For flux-free radially symmetric magnetic fields defined on circular regions, we establish that particle escape speeds…