Related papers: Gauss Optics and Gauss Sum on an Optical Phenomena
We develop a unified formalism for describing the interaction of gravitational waves with matter that clearly separates the effects of general relativity from those due to interactions in the matter. Using it, we derive a general expression…
It is well known that the classical Gauss sum, normalized by the square-root number of terms, takes only finitely many values. If one restricts the range of summation to a subinterval, a much richer structure emerges. We prove a limit law…
We discuss polarization of gravitational radiation within the standard framework of linearized general relativity. The recent experimental discovery of gravitational waves provides the impetus to revisit the implications of the…
In this paper we construct a geometric analogue of the Weil representation over a finite field. Our construction is principally invariant, not choosing any specific realization. This eliminates most of the unpleasant formulas that appear in…
The laws of geometric optics and their corrections are derived for scalar, electromagnetic, and gravitational waves propagating in generic curved spacetimes. Local peeling-type results are obtained, where different components of…
In this talk I present some of the recent theoretical results that have been obtained on glassy systems like spin glasses or structural glasses. The physical principles at the basis of the theory are explained in a simple language (without…
We consider the distribution of quadratic Gauss paths, polygonal paths joining partial sums of quadratic Gauss sums to square-free fundamental discriminant moduli in a dyadic range [Q,2Q]. We prove that this striking ensemble converges in…
The field diffracted from a one-dimensional, coherently illuminated periodic structure at fractional Talbot distances can be described as a coherent sum of shifted units cells weighted by a set of phases given by quadratic Gauss sums. We…
Understanding of Weyl gauge symmetry is rarely associated with underlying postulates. Here we show that such an omission leads to discrepancies in regard to the reach and consequences of gauge symmetry within gravitational theories.…
Based on the reciprocity theorem, we present a formalism to calculate the power emitted by a dipole source into a particular propagating mode leaving an open optical system. The open system is completely arbitrary and the approach can be…
In this paper the Gaussian integral is proven using contour integration on $\frac{1}{e^{x^2}+1}$ and linking it using a limit to said Gaussian integral. The limit is alsorelated to the Riemann Zeta function using a few manipulations. This…
We discuss the wave optical effects in gravitational lens systems with two point mass lenses in two different lens planes. We identify and vary parameters (i.e., lens masses, related distances, and their alignments) related to the lens…
One-dimensional optical waveguiding is revisited using the electromagnetic deduction of Fresnel formulas relating the incident, reflected, and transmitted waves on the abrupt interface between two different optical media. Throughout the…
Quantum optics with quantum gases represents a new field, where the quantum nature of both light and ultracold matter plays equally important role. Only very recently this ultimate quantum limit of light-matter interaction became feasible…
In this paper, we introduce the method of adding additional factors and a parameter to multiple zeta values and prove some generalizations of the duality theorem and several relations among multiple zeta values. In particular, we are able…
Some class of sums which naturally include the sums of powers of integers is considered. A number of conjectures concerning a representation of these sums is made.
In the present manuscript, I examine an intriguing relation at the classical level between general relativity and a theory where matter couples uniquely multiplicatively to geometry in the Lagrangian density. Interestingly, the…
When gravitational waves propagate near massive objects, their paths curve resulting in gravitational lensing, which is expected to be a promising new instrument in astrophysics. If the time delay between different paths is comparable with…
The lensing of gravitational waves (GWs) occurs when GWs experience local gravitational potential. In the weak lensing regime, it has been reported that a simple consistency relation holds between the variances of the magnification and…
For various classes of graphical models it has been observed that the ratio of the partition sum to its Bethe approximation is often close to being the square of the ratio of the partition sum to its degree-2 Bethe approximation. This is of…