Related papers: Two paths towards circulation time derivative (Max…
Gill and Zachary's proper-time reformulation of Maxwell's equations introduces a source-dependent speed b = sqrt(c^2 + u^2), distinct from standard electrodynamics. This study applies Lie symmetry analysis to the resulting wave equations,…
We show that Maxwell's electrodynamics in vacuum is invariant under active transformations of the metric. These metrics are related by disformal mappings induced by derivatives of the gauge vector $A_{\mu}$ such that the gauge symmetry is…
We prove that a $4d$ theory of non-linear electrodynamics has equations of motion which are equivalent to those of the Maxwell theory in curved spacetime, but with the usual metric $g_{\mu \nu}$ replaced by a unit-determinant metric $h_{\mu…
Many practical applications exploit an external local magnetic field -- magnetic obstacle -- as an essential part of their constructions. Recently, it has been demonstrated that the flow of an electrically conducting fluid influenced by an…
Carter derived the forms of the metric and the vector potentials of the space-times in which the relativistic Schrodinger equation for the motion of a charged particle separates. Here we show that on each `spheroidal' surface a rotation…
For a periodically driven quantum system an effective time-independent Hamiltonian is derived with an eigen-energy spectrum, which in the regime of large driving frequencies approximates the quasi-energies of the corresponding Floquet…
We derive the Abraham-Lorentz-Dirac (ALD) equation in the framework of the electrodynamic theory associated with Stueckelberg manifestly covariant canonical mechanics. In this framework, a particle worldline is traced out through the…
While the vast majority of calculations reported on molecular conductance have been based on the static non-equilibrium Green's function formalism combined with density functional theory, in recent years a few time-depedent approaches to…
It is generally accepted that the dynamics of relativistic particles in the lab frame can be described by taking into account the relativistic dependence of the particles momenta on the velocity, with no reference to Lorentz…
The paper focuses on applying the algebra of octonions to explore the influence of electric-charge gradients on the electric-current derivatives, revealing some of major influence factors of high pulse electric-currents. J. C. Maxwell was…
Starting from the Dirac equation in external electromagnetic and torsion fields we derive a path integral representation for the corresponding propagator. An effective action, which appears in the representation, is interpreted as a…
Ballistic transport properties in a two dimensional electron gas are studied numerically, where magnetic fields are perpendicular to the plane of two dimensional electron systemsand periodically modulated both in $x$ and $y$ directions. We…
We are interested in the motion of a classical charge coupled to the Maxwell self-field and subject to a uniform external magnetic field, B. This is a physically relevant, but difficult dynamical problem, to which contributions range over…
A new formulation of the Maxwell equations based on two vector and two scalar potentials is proposed. The use of these potentials allows the electromagnetic field equations to be written in the form of a hyperbolic system. In contrast to…
We study the motion of a charged particle under the action of a magnetic field with cylindrical symmetry. In particular we consider magnetic fields with constant direction and with magnitude depending on the distance $r$ from the symmetry…
A novel radially local approximation of the drift kinetic equation is presented. The new drift kinetic equation that includes both ${\bf E} \times {\bf B}$ and tangential magnetic drift terms is written in the conservative form and it has…
Albeit the past intensive research, the governing equation of anomalous diffusion which is observed for the transport of particles underground is still an open problem. In this paper, as a governing equation, the advection-diffusion…
The control of any type of quantum hardware invariably necessitates time-dependent driving. If the basis depends on the control parameter, the presence of a time-dependent control field yields an extra term in the Schr\"odinger equation…
In \cite{2} it was shown that Einstein's special theory of relativity and Maxwell's field theory have mathematically equivalent dual versions. The dual versions arise from an identity relating observer time to proper time as a contact…
It is pointed out that the usual derivation of the well-known Maxwell electromagnetic equations holds only for a medium at rest. A way in which the equations may be modified for the case when the mean flow of the medium is steady and…