Related papers: Gauss Optics and Gauss Sum on an Optical Phenomena
We solve an elementary number theory problem on sums of fractional parts, using methods from group theory. We apply our result to deduce the finiteness of certain monodromy representations.
Gravitational waves propagating across gravitational potentials undergo lensing effects that, in the wave-optics regime, manifest as frequency-dependent amplitude and phase modulations. In this work, we revisit the diffraction integral…
We consider alternative orders of summation for the conditionally convergent series defining the weight-2 Eisenstein series G2 and the Weierstrass p-function. The resulting sums differ from the standard ones by a residual term that can be…
Like light, gravitational waves are gravitationally lensed by intervening massive astrophysical objects, such as galaxies, clusters, black holes, and stars, resulting in a variety of potentially observable gravitational-wave lensing…
Wave-mechanical effects in gravitational lensing have long been predicted, and with the discovery of populations of compact transients such as gravitational wave events and fast radio bursts, may soon be observed. We present an observer's…
All prior applications of Diffusing-Wave Spectroscopy (DWS) to aqueous foams rely upon the assumption that the electric field of the detected light is a Gaussian random variable and that, hence, the Siegert relation applies. Here we test…
We introduce and study a generalized energy conservation relation for scattering of time-modulated waves, where conventional energy conservation does not hold. Based on this relation, we derive an optical theorem and compute the active…
We study reciprocity formulas for Dedekind sums associated with absolutely continuous functions, extending the classical Dedekind-Rademacher reciprocity formula. In particular, we treat the case of periodic Bernoulli functions. Our approach…
For a system with a fixed number of electrons, the total optical sum is a constant, independent of many-body interactions, of impurity scattering and of temperature. For a single band in a metal, such a sum rule is no longer independent of…
We briefly review Artin's reciprocity law in the classical ideal theoretic language, and then study connections between Artin's reciprocity law and the proofs of the quadratic reciprocity law using Gauss's Lemma.
Symmetry and reciprocity constraints on polarization state of the field diffracted by gratings of quasi-planar particles are considered. It is shown that the optical activity effects observed recently in arrays of quasi-planar plasmonic…
Significant absorption of radiation is usually accompanied by refraction. This is not the case for $\gamma$ rays travelling cosmic distances. We show that the real and imaginary parts of the refraction index are indeed commensurable, as…
An approach to special relativity is outlined which emphasizes the wave and field mechanisms which physically produce the relativistic effects, with the goal of making them seem more natural to students by connecting more explicitly with…
In this paper some links between the density of a set of integers and the density of its sumset, product set and set of subset sums are presented.
In this paper we discuss some of the mathematical and numerical issues that have to be addressed when calculating wave scattering using the EOS approach. The discussion is framed in context of light scattering by objects whose optical…
Probing the polarization of gravitational waves (GWs) would provide an evidence of graviton, indicating the quantization of gravity. Motivated by the next generation of gravitational wave detectors, we make an attempt to study the possible…
Concepts like peculiar velocity, gravitational force, and power spectrum and their interrelationships are of utmost importance in the theories of structure formation. The observational implementation of these concepts is usually based on…
The complementary wave and particle character of quantum objects (or quantons) was pointed out by Niels Bohr. This wave-particle duality, in the context of the two-slit experiment, is now described not just as two extreme cases of wave and…
Gravitational lensing magnification is maximal around caustics. At these source locations, an incoming wave from a point source would formally experience an infinite amplification in the high-frequency or geometric optics limit. This…
We define the notion of mutual quantum measurements of two macroscopic objects and investigate the effect of these measurements on the velocities of the objects. We show that multiple mutual quantum measurements can lead to an effective…