Related papers: Asymmetric Cauchy-Riemann Beams
We study the effects of the quantum vacuum on the propagation of a Gaussian laser beam in vacuum. By means of a double perturbative expansion in paraxiality and quantum vacuum terms, we provide analytical expressions for the self-induced…
We investigate three-dimensional nonparaxial linear accelerating beams arising from the transverse Whittaker integral. They include different Mathieu, Weber, and Fresnel beams, among other. These beams accelerate along a semicircular…
A new approach to the modeling of nonfree particle diffusion is presented. The approach uses a general setup based on geometric graphs (networks of curves), which means that particle diffusion in anything from arrays of barriers and pore…
We show that propagating optical fields bearing an axial symmetry are not truly hollow in spite of a null electric field on-axis. The result, obtained by general arguments based upon the vectorial nature of electromagnetic fields, is of…
The nonperturbative fermion-boson vertex function in four-dimensional Abelian gauge theories is self-consistently and exactly derived in terms of a complete set of normal (longitudinal) and transverse Ward-Takahashi relations for the The…
A quantum state of an electron influences its electromagnetic field. If a spatial profile of the electron wave packet is not Gaussian, the particle may acquire additional intrinsic multipole moments, which alter its field, especially at…
We consider the Cauchy problem for doubly nonlinear degenerate parabolic equations with inhomogeneous density on noncompact Riemannian manifolds. We give a qualitative classification of the behavior of the solutions of the problem depending…
In this paper, we study the geometric nonlinearity properties, such as curvature and torsion, in a dual coordinate system of the Riemannian manifold defined by the Gaussian distribution. We also give the Amari formulas explicitly in this…
Bayesian methods are developed for the multivariate nonparametric regression problem where the domain is taken to be a compact Riemannian manifold. In terms of the latter, the underlying geometry of the manifold induces certain symmetries…
In this work, we extend the analytic treatment of Bessel functions of large order and/or argument. We examine uniform asymptotic Bessel function expansions and show their accuracy and range of validity. Such situations arise in a variety of…
In this paper, we consider the fractional Camassa-Holm equation modelling the propagation of small-but-finite amplitude long unidirectional waves in a nonlocally and nonlinearly elastic medium. First, we establish the local well-posedness…
We consider the Cauchy problem for systems of nonlinear wave equations with multiple propagation speeds in three space dimensions. Under the null condition for such systems, the global existence of small amplitude solutions is known. In…
We study the impact on shape parameters of an underlying Bienaym\'e-Galton-Watson branching process (height, width and first hitting time), of having a non-spatial branching mechanism with infinite variance. Aiming at providing a…
Scalar theory of quantum electron beam optics, at the single-particle level, derived from the Dirac equation using a Foldy-Wouthuysen-like transformation technique is considered. Round magnetic electron lenses with Glaser and power law…
In this work, we study probability functions associated with Gaussian mixture models. Our primary focus is on extending the use of spherical radial decomposition for multivariate Gaussian random vectors to the context of Gaussian mixture…
We investigate the spectral degree of freedom of OAM-carrying localized waves, and its influence on their transverse intensity distribution. In particular, we focus our attention on two different families of spectra, namely exponentially…
We study the dynamics of fast two-beam collisions in linear optical media with weak cubic loss in spatial dimension higher than 1. For this purpose, we extend the perturbation theory that was developed for analyzing two-pulse collisions in…
Gaussian beams describe the amplitude and phase of rays and are widely used to model acoustic propagation. This paper describes four new results in the theory of Gaussian beams. (1) A new version of the \v{C}erven\'y equations for the…
We give an exact self-consistent operator description of the spin and orbital angular momenta, position, and spin-orbit interactions of nonparaxial light in free space. Both quantum-operator formalism and classical energy-flow approach are…
Utilizing the extended Huygens-Fresnel principle and the Rytov approximation, the analytical formula for the propagation of a partially coherent electromagnetic hyperbolic-sine-Gaussian vortex beam (PCEShVB) in anisotropic atmospheric…