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It is common practice to estimate the errors on the angular power spectrum which could be obtained by an experiment with a given angular resolution and noise level. Several authors have also addressed the question of foreground subtraction…
The idealized theory of quantum vacuum energy density is a beautiful application of the spectral theory of differential operators with boundary conditions, but its conclusions are physically unacceptable. A more plausible model of a…
We present results from an end-to-end simulation pipeline interferometric observations of cosmic microwave background polarization. We use both maximum-likelihood and Gibbs sampling techniques to estimate the power spectrum. In addition, we…
We prove a Weyl-type fractal upper bound for the spectrum of the damped wave equation, on a negatively curved compact manifold. It is known that most of the eigenvalues have an imaginary part close to the average of the damping function. We…
With the rapid development of microwave photonics, which has expanded to numerous applications of commercial importance, eliminating the emerging bottlenecks becomes of vital importance. For example, as the main branch of microwave…
We analytically show that probabilistic amplification of a weak coherent state stored inside an atomic medium can be achieved via detection of coherently scattered photons. We show that this is because of collective excitations created…
In combination with post-selection, weak measurements can lead to surprising results known as anomalous weak values. These lie outside the bounds of the spectrum of the relevant observable, as in the canonical example of measuring the spin…
The relativistic quantum equation is proposed for the complex wave function, which has the meaning of a probability amplitude. The Lagrangian formulation of the proposed theory is developed. The problem of spreading of a wave packet in an…
We approach wave particle duality, the role of the observer and implications on Retrocausality, by starting with the results of a well verified quantum experiment. We analyze how some current theoretical approaches interpret these results.…
We report our investigation on the input signal amplification in unidirectionally coupled monostable Duffing oscillators in one- and two-dimensions with first oscillator alone driven by a weak periodic signal. Applying a perturbation theory…
The average result of a weak measurement of some observable $A$ can, under post-selection of the measured quantum system, exceed the largest eigenvalue of $A$. The nature of weak measurements, as well as the presence of post-selection and…
I calculate the limitations on the widely-used forward-only (uni-directional) propagation assumption by considering the effects of transverse effects (e.g. diffraction). The starting point is the scalar second order wave equation, and…
Cross-spectral analysis is a mathematical tool for extracting the power spectral density of a correlated signal from two time series in the presence of uncorrelated interfering signals. We demonstrate and explain a set of conditions where…
We investigate a system of two weakly coupled oscillators. It is shown that an external periodic perturbation can lead to the capture into resonance. Asymptotic description and numerical simulations are presented. We have obtained the…
The search for faint emission or absorption lines in astronomical spectra has received considerable attention in recent years, especially in the X-ray wavelength range. These features usually appear as a deficit or excess of counts in a…
The general method to obtain solutions of the Maxwellian equations from scalar representatives is developed and applied to the diffraction of electromagnetic waves. Kirchhoff's integral is modified to provide explicit expressions for these…
For over 70 years it has been assumed that scalar wave propagation in (ensemble-averaged) random particulate materials can be characterised by a single effective wavenumber. Here, however, we show that there exist many effective…
Since its introduction 25 years ago, the quantum weak value has gradually transitioned from a theoretical curiosity to a practical laboratory tool. While its utility is apparent in the recent explosion of weak value experiments, its…
An algorithm is presented which generates pairs of oscillatory random time series which have identical periodograms but differ in the number of oscillations. This result indicate the intrinsic limitations of spectral methods when it comes…
An envelope function approach is used to study the wave propagation in a one-dimensional Photonic Crystal containing single negative layers. This approach enables one to obtain the analytic expressions of the parameters of an equivalent…