Related papers: Vector spherical quasi-Gaussian vortex beams
We investigate high-order Convolution Quadratures methods for the solution of the wave equation in unbounded domains in two dimensions that rely on Nystr\"om discretizations for the solution of the ensemble of associated Laplace domain…
This work is concerned with the construction of Gaussian Beam (GB) solutions for the numerical approximation of wave equations, semi-discretized in space by finite difference schemes. GB are high-frequency solutions whose propagation can be…
The recognition in the 1990s that vortex beams (VBs), paraxial light beams with optical vortices, carry orbital angular momentum (OAM), has benefited applications ranging from optical manipulation to high-dimensional classical and quantum…
We study the electronic structure in the vicinity of a vortex in a two-band superconductor in which the quasiparticle motion is ballistic in one band and diffusive in the other. This study is based on a model appropriate for such a case,…
We present a method for the realization of radially and azimuthally polarized nonparaxial Bessel beams in a rigorous but simple manner. This result is achieved by using the concept of Hertz vector potential to generate exact vector…
We propose the frozen Gaussian approximation for computation of high frequency wave propagation. This method approximates the solution to the wave equation by an integral representation. It provides a highly efficient computational tool…
The virial expansion provides a non-perturbative view into the thermodynamics of quantum many-body systems in dilute regimes. While powerful, the expansion is challenging as calculating its coefficients at each order $n$ requires analyzing…
We introduce new finite-dimensional spaces specifically designed to approximate the solutions to high-frequency Helmholtz problems with smooth variable coefficients in dimension $d$. These discretization spaces are spanned by Gaussian…
A new approximation scheme for nonperturbative renormalisation group equations for quantum gravity is introduced. Correlation functions of arbitrarily high order can be studied by resolving the full dependence of the renormalisation group…
Let g be a semisimple Lie algebra with h a Cartan subalgebra. The orbit method attempts to assign representations of g to orbits in g*. Orbital varieties are particular Lagrangian subvarieties of such orbits which should lead to highest…
Let ${\mathfrak{G}}\subset\mathbb{R}^{3}$ with $vol(\mathfrak{G})\sim L^{3}$. Let ${\mathscr{T}}(x)$ be a Gaussian random field $\forall~x\in\mathfrak{G}$ with expectation $\mathbf{E}[{\mathscr{T}}(x)]=0$ and correlation…
In the present paper we develop an algorithm to solve the time dependent Ginzburg-Landau (TDGL) equations, by using the link variables technique, for circular geometries. In addition, we evaluate the Helmholtz and Gibbs free energy, the…
Bogoliubov quasiparticles play a crucial role in understanding the behavior of a superconductor, and in achieving reliable operations of superconducting quantum circuits. Diagnosis of quasiparticle poisoning at the nanoscale provides…
We deal with planar vortex structures in Maxwell-Higgs models in the presence of a generalized magnetic permeability. The model under investigation engenders a real parameter that controls the behavior of the tail of the solutions and of…
Asymptotic behavior of the scattering amplitude for two scalar particles by scalar, vector and tensor exchanges at high energy and fixed momentum transfers is reconsidered in quantum field theory. In the framework of the quasi-potential…
Generation and detection of structured light have recently been the subject of intense study, aiming to realize high-capacity optical storage and continuous-variable quantum technologies. Here, we present a scheme to extract the orbital…
We present a Virtual Element Method (VEM) for the solution of Dirichlet problems for the quasilinear equation $-\text{div} (k(u)\text{grad} u)=f$ with essential boundary conditions. Within the VEM the nonlinear coefficient is evaluated with…
Multipole expansion of an incident radiation field - that is, representation of the fields as sums of vector spherical wavefunctions - is essential for theoretical light scattering methods such as the T-matrix method and generalised…
We associate cube complexes called completions to each subgroup of a right-angled Coxeter group (RACG). A completion characterizes many properties of the subgroup such as whether it is quasiconvex, normal, finite-index or torsion-free. We…
We deal with the virtual element method (VEM) for solving the Poisson equation on a domain $\Omega$ with curved boundaries. Given a polygonal approximation $\Omega_h$ of the domain $\Omega$, the standard order $m$ VEM [6], for $m$…