Related papers: Exact elegant Laguerre-Gaussian vector wave packet…
We develop a method to compute the moments of the eigenvalue densities of matrices in the Gaussian, Laguerre and Jacobi ensembles for all the symmetry classes beta = 1,2, 4 and finite matrix dimension n. The moments of the Jacobi ensembles…
We consider the quantum theory of paraxial non-relativistic electron beams in non-uniform magnetic fields, such as the Glaser field. We find the wave function of an electron from such a beam and show that it is a joint eigenstate of two…
A semi-analytical computational algorithm to model the wavefield generated by paraxial diffraction of a class of Laguerre-Gauss beams by sharp-edge elliptic apertures is here developed. Thanks to such a powerful computational tool, some…
We explore the spectral properties of the time-dependent Maxwell's equations for a plane interface between a metamaterial represented by the Drude model and the vacuum, which fill respectively complementary half-spaces. We construct…
A theory is presented (and supported by numerical simulations) for phase-coherent reflection of light by a disordered medium which either absorbs or amplifies radiation. The distribution of reflection eigenvalues is shown to be the Laguerre…
Let U be a real form of a complex semisimple Lie group, and tau, sigma, a pair of commuting involutions on U. This data corresponds to a reflective submanifold of a symmetric space, U/K. We define an associated integrable system, and…
The equation is considered for a composite scalar particle with polarizabilities in an external quantized electromagnetic plane wave. This equation is reduced to a system of equations for infinite number of interacting oscillators. After…
Efficient electronic structure methods can be built around efficient tensor representations of the wavefunction. Here we describe a general view of tensor factorization for the compact representation of electronic wavefunctions. We use…
Motivated by the study of wave fronts in anisotropic media, we propose an incidence geometry of anisotropic spheres in a Finsler-Minkowski space. An anisotropic version of the Laguerre functional is considered. In some circumstances, this…
We explicitly prove that the transfer matrix of a finite layered $PT$-symmetric system of fix length $L$ consisting of $N$ units of the potential system `$+iV$' and `$-iV$' of equal thickness becomes a unit matrix in the limit $N…
A simple exact covariant model in which a scalar particle is modeled as a bound state of two different particles is used to elucidate relativistic aspects of electromagnetic form factors. The model form factor is computed using an exact…
We investigate the phenomenon of the transverse breaking of symmetry of Gaussian lasers transmitted through dielectrics, showing for which incidence conditions and beam parameters it can be observed in optical experiments. The numerical…
In a previous communication (W.J.T. Bos and J.-P. Bertoglio 2006, Phys. Fluids, 18, 031706), a self-consistent Markovian triadic closure was presented. The detailed derivation of this closure is given here, relating it to the Direct…
We report on the fabrication of metasurface phase plates consisting of gold nanoantenna arrays that generate Laguerre-Gaussian modes from a circularly polarized Gaussian input beam. The corresponding helical phase profiles with radial…
The Laguerre functions constitute one of the fundamental basis sets for calculations in atomic and molecular electron-structure theory, with applications in hadronic and nuclear theory as well. While similar in form to the Coulomb…
By studying the development of shock waves out of discontinuity waves, in 1954 P. Lax discovered a class of PDEs, which he called 'completely exceptional', where such a transition does not occur after a finite time. A straightforward…
The wave function of a composite system is defined in relativity on a space-time surface. In the explicitly covariant light-front dynamics, reviewed in the present article, the wave functions are defined on the plane $\omega \cd x=0$, where…
We introduce a general implementation of the recently proposed homogenization theory [Tsukerman, J. Opt. Soc. Am. B 28, 577 (2011)] allowing one to retrieve all 36 linear constitutive parameters of any 3D metamaterial with parallelepipedal…
We consider the problem of parameter estimation in a high-dimensional generalized linear model. Spectral methods obtained via the principal eigenvector of a suitable data-dependent matrix provide a simple yet surprisingly effective…
We present a method to calculate exact dynamics of a wave-packet in a quantum two-state problem with Dirac delta coupling. The advantage of our method is that the calculations are done in the time domain. Hence inverting the solutions from…