Related papers: Simple wave-optical superpositions as prime number…
Prime number related fractal polygons and curves are derived by combining two different aspects. One is an approximation of the prime counting function build on an additive function. The other are prime number indexed basis entities taken…
By following the trajectories of quantum particles inside a periodic lattice and preserving their classical probabilities for reflection, transmission and absorption at each lattice plane, classical scattering outcomes are obtained.…
Dirichlet's theorem guarantees infinitely many primes in each reduced residue class modulo q, but the analytic mechanism underlying this separation is often difficult to visualize directly. In this article we construct simplified…
We consider the representation of primes as a sum of a prime and twice a triangular number. We prove that a subset of the primes having density 1 is expressible in this form. We conjecture that every odd prime number is expressible as a sum…
We are interested in classifying those sets of primes $\mathcal{P}$ such that when we sieve out the integers up to $x$ by the primes in $\mathcal{P}^c$ we are left with roughly the expected number of unsieved integers. In particular, we…
Permutation Matrices are a well known class of matrices which encode the elements of the symmetric group on $d$ elements as a square $d\times d$ matrix. Motivated by [4], we define a similar class of matrices which are a generalization of…
Optical mixing experiments show the ability of amplifying a weak optical signal by superposing it with a stronger one. This principle has been demonstrated also for weak signals at the quantum level, down to a single photon. In the present…
The distribution of differences of consecutive members of sequences of primes is investigated. A quantitative measure for oscillations among these differences is the curvature of the sequence. If the sequence is not too sparse, then sharp…
We consider wave propagation problems over 2-dimensional domains with piecewise-linear boundaries, possibly including scatterers. We assume that the wave speed is constant, and that the initial conditions and forcing terms are radially…
Assuming the Riemann Hypothesis we obtain asymptotic estimates for the mean value of the number of representations of an integer as a sum of two primes. By proving a corresponding Omega-term, we prove that our result is essentially the best…
Two approaches (micro- and macro- investigations) are used to determine the dimension dependences of the optical parameters of the nanometer-scale layers of materials. It is shown that both an index of refraction and coefficient of…
We describe the resonant interaction of an atom with a strongly focused light beam by expanding the field in multipole waves. For a classical field, or when the field is described by a coherent state, we find that both intensity pattern and…
For a random field on a general discrete set, we introduce a condition that the range of the correlation from each site is within a predefined compact set D. For such a random field omega defined on the model set Lambda that satisfies a…
We trap a single cesium atom in a standing-wave optical dipole trap. Special experimental procedures, designed to work with single atoms, are used to measure the oscillation frequency and the atomic energy distribution in the dipole trap.…
A scheme for control and read-out of diffracted spins waves to propagating light fields is presented. Diffraction is obtained via sinusoidally varying lights shifts and ideal one-to-one mapping to light is realized using a gradient echo…
Gravitational waves are a unique probe of the early Universe, as the Universe is transparent to gravitational radiation right back to the end of inflation. In this article, we summarise detection prospects and the wide scope of primordial…
We study, from the viewpoint of metrical number theory and (infinite) ergodic theory, the probabilistic laws governing the occurrence of prime numbers as digits in continued fraction expansions of real numbers.
We present a simple, closed formula which gives all the primes in order. It is a simple product of integer floor and ceiling functions.
The refraction of light by dispersion-free dielectric media can be modeled using well-localized macroscopic wave packets, enabling a description in terms of pseudo-particles. This approach is often used in thought experiments to illustrate…
In this document we consider the prime spectrum of an MV-algebra with certain natural operations. These are used to show connections between the classes of prime lattice filters and prime implication filters.