Related papers: Displacement Current in Classical and Quantum Syst…
This article serves as a pedagogical introduction to the problem of motion in classical field theories. The primary focus is on self-interaction: How does an object's own field affect its motion? General laws governing the self-force and…
We establish, in general terms, the conditions to be satisfied by a time-fractional approach formulation of the Poisson-Nernst-Planck model in order to guarantee that the total current across the sample be solenoidal, as required by the…
The time derivative of the circulation of a vector field $\boldsymbol{A}$ over a moving and deforming closed curve, $\frac {\mathrm{d}}{\mathrm{d} t}\oint \boldsymbol{A} \cdot \mathrm{d} \boldsymbol{r}$, is computed in two ways, with and…
Electrodynamics is usually written with a polarization vector field to describe the response of matter to electric fields, or more specifically, to describe changes in distribution of charge as an electric field is changed. This approach…
A derivation is presented of the quantummechanical wave equations based upon the Equity Principle of Einstein's General Relativity Theory. This is believed to be more generic than the common derivations based upon Einstein's energy…
Causality in electrodynamics is a subject of some confusion, especially regarding the application of Faraday's law and the Ampere-Maxwell law. This has led to the suggestion that we should not teach students that electric and magnetic…
Maxwell Electrodynamics can be described either in Minkowski space-time or in a dynamically equivalent way in a curved geometry constructed in terms of the electromagnetic field. For this the field must have a superior bound limited by a…
We demonstrate how to derive Maxwell's equations, including Faraday's law and Maxwell's correction to Amp\`ere's law, by generalizing the description of static electromagnetism to dynamical situations. Thereby, Faraday's law is introduced…
Despite the many successes of the relativistic quantum theory developed by Horwitz, et. al., certain difficulties persist in the associated covariant classical mechanics. In this paper, we explore these difficulties through an examination…
The mean square displacement $\langle\left(x(t)-x(0)\right)^2\rangle$ of the position $x$ of a free particle of mass $m$ at thermal equilibrium is evaluated quantum mechanically. An analytical expression is obtained which shows an initial…
It is now widely accepted that the Maxwell equations of Electrodynamics constitute a self-consistent set of four independent partial differential equations. According to a certain school of thought, however, half of these equations -…
We consider a generalization of the classical nonrelativistic St\"{o}rmer problem, describing the motion of charged particles in a purely magnetic dipole field, by taking into account the effects of the dissipation, assumed to be of…
The distribution of the initial short-time displacements of particles is considered for a class of classical systems under rather general conditions on the dynamics and with Gaussian initial velocity distributions, while the positions could…
A Hamiltonian approach is presented to study the two dimensional motion of damped electric charges in time dependent electromagnetic fields. The classical and the corresponding quantum mechanical problems are solved for particular cases…
It is shown that the point charge and magnetic moment of electron produce together such a field that total electromagnetic momentum has a component perpendicular to electron velocity. As a result classical electron models, having magnetic…
We study a generic quantum Markovian master equation for a linearly displaced or driven harmonic oscillator. It was known that the displacement dynamics of Gaussian mixed states depends on the unitary part of the Liouvillian, the decay rate…
Unlike a single Carroll particle, a multiparticle Carroll system can move under suitable conditions, as we demonstrate it explicitly for two particles with a momentum-dependent interaction: the center-of-mass remains fixed, however relative…
We further develop a recently introduced variational principle of stationary action for problems in nonconservative classical mechanics and extend it to classical field theories. The variational calculus used is consistent with an initial…
We contrast two sets of conditions that govern the transition in which classical dynamics emerges from the evolution of a quantum system. The first was derived by considering the trajectories seen by an observer (dubbed the ``strong''…
A theory is presented for calculating the effect of the electromagnetic field on the centre of mass of a macroscopic dielectric body that is valid in both quantum and classical regimes. We apply the theory to find the classical equation of…