相关论文: Deducing the Talbot Effect from Electrodynamics
We analyze the stability of Maxwell equations in bounded domains taking into account electric and magnetization effects. Well-posedness of the model is obtained by means of semigroup theory. A passitivity assumption guarantees the…
The aim of this article is to show how certain parabolic theorems follow from their elliptic counterparts. This technique is demonstrated through new proofs of five important theorems in parabolic unique continuation and the regularity…
The Grad method is generalized based on the Bogolyubov idea of the functional hypothesis for states at the end of relaxation processes in a system. The Grad problem (i.e., description of the Maxwell relaxation) for a completely ionized…
Recently there has been a renewed interest in axionic generalization of electrodynamics due to its application to topological insulators. A low-energy electromagnetic response of these exotic materials was proposed to be described by an…
We applied an effective approximation into Maxwell's equations with an axion interaction for haloscope searches. A set of Maxwell's equations acquired from this approximation describes just the reacted fields generated by the anomalous…
Formal analogies between gravitational and optical phenomena have been explored for over a century, providing valuable insights into kinematic aspects of general relativity. Here, this analogy is employed to study light propagation in…
In this communication, the derivation of the Boltzmann-Gibbs and the Maxwellian distributions is presented from a geometrical point of view under the hypothesis of equiprobability. It is shown that both distributions can be obtained by…
We introduce elliptic weights of boxed plane partitions and prove that they give rise to a generalization of MacMahon's product formula for the number of plane partitions in a box. We then focus on the most general positive degenerations of…
We consider the time dependent Maxwell system in the sense of distributions in the context of temporal interfaces. Just as with spatial interfaces, electromagnetic waves at temporal interfaces scatter and create a transmitted and reflected…
The purpose of this note is to see to what extent ideal gas laws can be obtained from simple Newtonian mechanics, specifically elastic collisions. We present simple one-dimensional situations that seem to validate the laws. The first…
This paper suggests an axiomatic approach to Maxwell's equations. The basis of this approach is a theorem formulated for two sets of functions localized in space and time. If each set satisfies a continuity equation then the theorem…
The analytical method of solving the boundary problems for a system of equations describing the behaviour of electrons and an electric field in the Maxwell plasma half-space is developed. Here the diffusion reflection of electrons from the…
We utilize exponential sum techniques to obtain upper and lower bounds for the fractal dimension of the graph of solutions to the linear Schr\"odinger equation on $\mathbb{S}^d$ and $\mathbb{T}^d$. Specifically for $\mathbb S^d$, we provide…
We obtain some "universal" estimates for $L_2$-norm of the solution of a parabolic equation via a weighted version of $H^{-1}$-norm of the free term. More precisely, we found the limit upper estimate that can be achieved by transformation…
A non-perturbative quantization of a paraxial electromagnetic field is achieved via a generalized dispersion relation imposed on the longitudinal and the transverse components of the photon wave vector. The theoretical formalism yields a…
Axion electrodynamics extends Maxwell's theory by postulating a hypothetical pseudoscalar axion field sourced by a scalar product of electric and magnetic fields. In this work, we demonstrate that a superposition of toroidal electromagnetic…
We describe electromagnetic propagation in a relativistic electron gas at finite temperatures and carrier densities. Using quantum electrodynamics at finite temperatures, we obtain electric and magnetic responses and general constitutive…
We provide several general versions of Littlewood's Tauberian theorem. These versions are applicable to Laplace transforms of Schwartz distributions. We apply these Tauberian results to deduce a number of Tauberian theorems for power series…
The excitation of plasmonic nanoparticles by incident electromagnetic waves at frequencies near their subwavelength resonances induces localized heat generation in the surrounding medium. We develop a mathematical framework to rigorously…
We propose a generalizing gauge-invariant model of propagating torsion which couples to the Maxwell field and to charged particles. As a result we have an Abelian gauge invariant action which leads to a theory with nonzero torsion and which…