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The NN scattering problem is usually analyzed in terms of partial waves and the corresponding coupled channel phase-shifts and mixing angles, but the available experiments induce correlations amongst the corresponding channels with…
A numerical-relativity calculation yields in general a solution of the Einstein equations including also a radiative part, which is in practice computed in a region of finite extent. Since gravitational radiation is properly defined only at…
Optical quantum routers play a crucial role in quantum networks and have been extensively studied in both theory and experiment, leading to significant advancements in their performance. However, these routers impose stringent requirements…
Rotating waves are a fascinating feature of a wide array of complex systems, particularly those arising in the study of many chemical and biological processes. With many rigorous mathematical investigations of rotating waves relying on the…
We propose a mathematical apparatus which converts magnetostatic (Walker) equations into a wave equation by introducing a specific definition of the magnetic refractive index. Its value can be manipulated by adjusting spatial distribution…
This paper revisits the topic of rotation estimation through the lens of special unitary matrices. We begin by reformulating Wahba's problem using $SU(2)$ to derive multiple solutions that yield linear constraints on corresponding…
We consider the gravity interacting with matter scalar fields and quantized in the minisuperspace approach in which the wave functional is described by the Wheeler-DeWitt equations (WdW). Assuming the domination of the homogeneous and…
Refractive gravitational waves are a generalisation of impulsive waves on a null hypersurface in which the metric is discontinuous but a weaker continuity condition for areas holds. A simple example of a plane wave is examined in detail and…
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 study the convergence properties of the two-dimensional Rigorous Coupled Wave Approach (RCWA) for s-polarized monochromatic incident light. The RCWA is widely used to solve electromagnetic boundary-value problems where the relative…
This contribution is divided in two parts. The first part provides a text-book level introduction to gravitational radiation. The key concepts required for a discussion of gravitational-wave physics are introduced. In particular, the…
The WKB approximation plays an essential role in the development of quantum mechanics and various important results have been obtained from it. In this paper, we introduce another method, {\it the so-called uniform asymptotic…
The wavefunctional in quantum gravity gives an amplitude for 3-geometries and matter fields. The four-space is usually recovered in a semiclassical approximation where the gravity variables are taken to oscillate rapidly compared to matter…
Traditionally resonant interactions among short waves, with large real wave-numbers, were described statistically and only a small domain in spectral space with integer wave-numbers, discrete resonances, had to be studied separately in…
We derive the leading asymptotic approximation, for low angle {\theta}, of the Wigner rotation matrix elements $d^j_{m_1m_2}(\theta)$, uniform in $j,m_1$ and $m_2$. The result is in terms of a Bessel function of integer order. We…
We investigate exact nonlinear waves on surfaces locally approximating the rotating sphere for two-dimensional inviscid incompressible flow. Our first system corresponds to a beta-plane approximation at the equator and the second to a gamma…
High accuracy calculations of atomic properties require using long basis sets. In particular, it is necessary to include large number of partial waves and estimate truncation corrections. The convergence in partial waves is known to be…
Light-matter interaction inside an optical cavity and formation of polaritonic states have gained interest in the past decades as it has direct applications in many research fields. Different regimes of light-matter coupling have been…
The plane-wave approximation is widely used in the practical calculations concerning neutrino oscillations. A simple derivation of this approximation starting from the neutrino wave-packet framework is presented.
The rigoruos mathematical theory of the coupling and response of a spherical gravitational wave detector endowed with a set of resonant transducers is presented and developed. A perturbative series in ascending powers of the square root of…