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A fixed electric charge is an electric current relative to a moving magnetic field, so that it is subjected to the force of the moving magnetic field. This means that not only time-varying magnetic field produces electric field, but moving…
In 1948, Feynman showed Dyson how the Lorentz force and Maxwell equations could be derived from commutation relations coordinates and velocities. Several authors noted that the derived equations are not Lorentz covariant and so are not the…
In this paper, one of the major shortcomings of the conventional numerical approaches is alleviated by introducing the probabilistic nature of molecular transitions into the framework of classical computational electrodynamics. The main aim…
In the recent work~\cite{Wang:2021p2}, the author proposed the expanded Maxwell's equations for moving charged media system, which seems subtle. Considering a very short time, we can approximately define the inertial frame of reference. If…
In curved spacetime, Maxwell's equations can be expressed in forms valid in Minkowski background, with the effect of the metric (gravity) appearing as effective polarizations and magnetizations. The electric and magnetic (EM) fields depend…
We will use Watts's theorem together with Lenzing's characterization of finitely presented modules via commuting properties of the induced tensor functor in order to study commuting properties of Ext-covariant functors.
We study how the complexity of evolutionary dynamics in the classic MacArthur consumer-resource model depends on resource uptake and utilization rates. The traditional assumption in such models is that the utilization rate of the consumer…
We provide a theoretical framework to describe the nonequilibrium temporal dynamics of correlated electron systems for realistic system parameters and the consequent, often exponentially long time scales. It is based on an entirely…
A theory where the gravitational, Maxwell and Dirac fields (mathematically represented as particular sections of a convenient Clifford bundle) are supposed fields in Faraday's sense living in Minkowski spacetime is presented. In our theory…
A unified electrodynamic approach to the guided wave excitation by external sources in the waveguiding structures with bianisotropic media is developed. Effect of electric, magnetic, and magneto- electric losses in such media manifests…
In moving electromagnetic systems, electromagnetic momentum calculated from the vector potential is shown to be proportional to the field energy of the system. The momentum thus obtained is shown actually to be the same as derived from a…
Ions in channels have been imagined as hard balls in a macroscopic mechanical model, for a very long time. Hard balls interact by collisions in such models, randomly knocking each other on and off `binding' sites in thermal motion. But ions…
We study the renormalized energy-momentum tensor (EMT) of the inflaton fluctuations in rigid space-times during the slow-rollover regime for chaotic inflation with a mass term. We use dimensional regularization with adiabatic subtraction…
The parallel mutation-selection evolutionary dynamics, in which mutation and replication are independent events, is solved exactly in the case that the Malthusian fitnesses associated to the genomes are described by the Random Energy Model…
Very recently, the authors of [PRL {\bf 118} (2017) 021102] have shown that violation of energy-momentum tensor (EMT) could result in an accelerated expansion state via appearing an effective cosmological constant, in the context of…
One of the axioms of quantum field theory is the property of unitarity of the evolution operator. However, if one considers the quantum electrodynamics in the external field in the leading order of perturbation theory, one will find that…
Conformal field theories (CFT) play an important role in quantum field theories as they allow for exact studies that are hard to access without the conformal symmetries in place. A remarkable recent development is the application of…
The Displacement Current is a peculiar aspect of Maxwell's equation created by theoretical necessity only to be later validated through experimentation. We analyze the properties of the Displacement Current in the static condition of…
This lecture note describes how to set up and what is behind a magnetodynamic field simulation for an accelerator magnet. The relevant formulation of Maxwell's equations is derived. The formulation is discretized in space by the…
In this paper, we discuss the Maxwell equations in terms of differential forms, both in the 3-dimensional space and in the 4-dimensional space-time manifold. Further, we view the classical electrodynamics as the curvature of a line bundle,…