Related papers: Singular Mueller matrices
The aim of this paper is twofold. First, we introduce a new class of linearizations, based on the generalization of a construction used in polynomial algebra to find the zeros of a system of (scalar) polynomial equations. We show that one…
In a previous paper we showed how higher-order strong-field-QED processes in long laser pulses can be approximated by multiplying sequences of "strong-field Mueller matrices". We obtained expressions that are valid for arbitrary field shape…
Idempotent elements play a fundamental role in ring theory, as they encode significant information about the underlying algebraic structure. In this paper, we study idempotent matrices from two perspectives. First, we analyze the partially…
An explanation of polarization entanglement is presented using Maxwells classical electromagnetic theory.Two key features are required to understand these classical origins.The first is that all waves diffract and weakly diffracting…
Recent experiments on electron scattering through molecular films have shown that chiral molecules can be efficient sources of polarized electrons even in the absence of heavy nuclei as source of a strong spin-orbit interaction. We show…
A new theory is presented for the development of circular polarization as radio waves propagate through the turbulent, birefringent interstellar medium. The fourth order moments of the wavefield are calculated and it is shown that…
Our aim is to explain instances in which the value of the logarithmic Mahler measure of a polynomial can be written in an unexpectedly neat manner. To this end we examine polynomials defining rational curves, which allows their zero-locus…
We elaborate the idea that the matrix models equipped with the gauge symmetry provide a natural framework to describe identical particles. After demonstrating the general prescription, we study an exactly solvable harmonic oscillator type…
Given a family of pairs of modules parametrised by a smooth space Y, the Multiplicity-Polar Theorem relates the multiplicity of the pair of modules at a special point of the parameter to the multiplicity of the pair at a generic point. This…
Dichroic filters are used by instrument designers to split a field of view into different optical paths for simultaneous measurement of different spectral bands. Quantifying the polarization aberrations of a dichroic is relevant for…
In General Relativity the metric can be recovered from the structure of the lightcones and a measure giving the volume element. Since the causal structure seems to be simpler than the Lorentzian manifold structure, this suggests that it is…
From the particle physics point of view, the most peculiar property of the dark matter particle is its stability on cosmological time scales. We briefly review the possible origins of this characteristic feature for candidates whose relic…
We give a self-contained exposition of some mathematical aspects of the Mueller-Stokes formalism. In the first part we review some basic notions of linear algebra and establish a proper notation. In the second part we introduce the…
The behavior of a massive scalar particle on the spacetime surrounding a monopole is studied from a quantum mechanical point of view. All the boundary conditions necessary to turn into self-adjoint the spatial portion of the wave operator…
The modular class of a regular foliation is a cohomological obstruction to the existence of a volume form transverse to the leaves which is invariant under the flow of the vector fields of the foliation. By drawing on the relationship…
Multi-frequency radio polarimetric observations of the diffuse Galactic synchrotron background enable us to study the structure of the diffuse ionized gas via rotation measure maps. However, depolarization will introduce artifacts in the…
Depolarization dyadics play a central role in theoretical studies involving scattering from small particles and homogenization of particulate composite materials. Closed-form expressions for depolarization dyadics have been developed for…
Small amplitude inhomogeneous plane waves propagating in any direction in a homogeneously deformed Hadamard material are considered. Conditions for circular polarization are established. The analysis relies on the use of complex vectors (or…
We analyze statistical properties of complex eigenvalues of random matrices $\hat{A}$ close to unitary. Such matrices appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with…
Based on work presented in [4], we define $S^2$-Upper Triangular Matrices and $S^2$-Lower Triangular Matrices, two special types of $d\times d(2d-1)$ matrices generalizing Upper and Lower Triangular Matrices, respectively. Then, we show…