Related papers: Line geometry and electromagnetism II: wave motion
A quantum-mechanical wave function is complex, but all observations are real, expressible through expectation values and transition matrix elements that involve the wave functions. It can be useful to separate at the outset the amplitude…
Following the spirit of de Broglie and Einstein, we think the concepts of matter and radiation can be unified. We know a particle propagates like a wave; its motion is described by certain wave equations. At this point, it is not clear what…
We describe a simple experimental apparatus which allows one to observe the wave properties of light in a new way. This apparatus also makes possible to introduce and illustrate, in a very suggestive way, some fundamental principles of…
The derivation of the equation of one-dimensional movement of a solitary shock wave is given. This derivation shows, that the differential equation of movement of a solitary plane shock wave in the channel with variable area, is exact, if…
Guided wave propagation through a left-handed medium has been studied, and new physics discovered. The results are based upon ab initio Green's function calculations. Numerically generated dispersion diagrams and field distribution plots…
Two-dimensional free-surface potential flows of an ideal fluid over a strongly inhomogeneous bottom are investigated with the help of conformal mappings. Weakly-nonlinear and exact nonlinear equations of motion are derived by the…
Quantum geometry of the electron wave function plays a significant role in the linear and non-linear responses of crystalline materials. Here, we study quantum geometry induced second harmonic generation. We identify non-linear responses…
Gauge theory underpins the quantum field theories of the standard model, and in a previous paper was shown via a geometric approach to describe classical electromagnetism in a form which approximates QED. Here we formalize and generalize…
In this paper, we extend the method developed in [17, 18] to curves in the Minkowski plane. The method proposes a way to study deformations of plane curves taking into consideration their geometry as well as their singularities. We deal in…
For acoustic waves in lined ducts, at given frequencies, the dispersion relation leads to a transcendental equation for the wavenumber that has to be solved by numerical methods. Based on Eckart explicit expression initially derived for…
In many physical situations involving diverse length scales, waves or rays representing them travel through media characterized by spatially smooth, random, modest refactive index variations. "Primary" diffraction (by individual…
Studying the geometry of sets appearing in various problems of quantum information helps in understanding different parts of the theory. It is thus worthwhile to approach quantum mechanics from the angle of geometry -- this has already…
We investigate in this chapter the mathematical models for electromagnetic wave propagation in dispersive isotropic passive linear media for which the dielectric permittivity $\varepsilon$ and magnetic permeability $\mu$ depend on the…
Geometry can fundamentally govern the propagation of light, independent of material constraints. Here, we demonstrate that a fractal phase space, endowed with a non-Euclidean, scale-dependent geometry, can intrinsically induce resonance…
The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical…
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…
A new version of the invariant imbedding theory for the propagation of coupled waves in inhomogeneous media is applied to the mode conversion of high frequency electromagnetic waves into electrostatic modes in cold, magnetized and…
Relativistically covariant form of equation of motion for real particle (neutral in charge) under the action of electromagnetic radiation is derived. Various formulations of the equation of motion in the proper frame of reference of the…
The role of frequency is very important in electromagnetics since it may significantly change how a material interacts with an incident wave if the frequency spectrum varies. Here, we demonstrate a new kind of microwave window that has the…
The paper shows the equivalence between the geometric frequency of an electric quantity, namely, voltage and current, and the Lagrange derivative of a stream-line of a fluid. The geometric frequency is a concept recently proposed by the…