Related papers: A Note on Spherical Needlets
This note corrects a technical error in Guardiola (2020, Journal of Statistical Distributions and Applications), presents updated derivations, and offers an extended discussion of the properties of the spherical Dirichlet distribution.…
The well-known spatial integration schemes in molecular electronic structure theory, immune to cusps and point singularities of some kind at atomic positions, use a set of weighting functions to split the integrand into a sum of…
The orthonormal set of Spherical Harmonics provides a natural way of expanding whole sky redshift and peculiar velocity surveys.
The mathematical representations of data in the Spherical Harmonic (SH) domain has recently regained increasing interest in the machine learning community. This technical report gives an in-depth introduction to the theoretical foundation…
We consider the selective sensing of planar waves in the presence of noise. We present different methods to control the sensitivity of a quantum sensor network, which allow one to decouple it from arbitrarily selected waves while retaining…
Electrodynamic spherical harmonic is a second rank tensor in three-dimensional space. It allows to separate the radial and angle variables in vector solutions of Maxwell's equations. Using the orthonormalization for electrodynamic spherical…
Recently, we have discovered a new concept of permanent wave resonance with potential spatial oscillations. This means the constant wave swinging frequency on the whole energy intervals of spectral forbidden zones destroying physical…
We introduce darning of compact sets (darning and gluing of finite unions of compact sets), which are not thin at any of their points, in a potential-theoretic framework which may be described, analytically, in terms of harmonic…
Spin squeezing has been explored in atomic systems as a tool for quantum sensing, improving experimental sensitivity beyond the spin standard quantum limit for certain measurements. To optimize absolute metrological sensitivity, it is…
In our recent paper [Phys. Rev. B 65, 075316 (2002)], the selection rules for the Raman scattering in spherical nanocrystals are analyzed. Here we show, that a physically expedient choice of the coordinate system, related to the…
A new characterization of harmonic functions is obtained. It is based on quadrature identities involving mean values over annular domains and over concentric spheres lying within these domains or on their boundaries. The analogous result…
Unusual scattering effects from tiny spherical particles may be obtained when concentric shells are designed by pairing together 'complementary' double-negative (DNG), single-negative (SNG), and/or standard double-positive (DPS) materials.…
Light scattering by small particles has a long and interesting history in physics. Nonetheless, it continues to surprise with new insights and applications. This includes new discoveries, such as novel plasmonic effects, as well as exciting…
The development of qualitatively new measurement capabilities is often a prerequisite for critical scientific and technological advances. The dramatic progress made by modern probe techniques to uncover the microscopic structure of matter…
Non-relativistic particles that are effectively confined to two dimensions can in general move on curved surfaces, allowing dynamical phenomena beyond what can be described with scalar potentials or even vector gauge fields. Here we…
This paper examines filtering on a sphere, by first examining the roles of spherical harmonic magnitude and phase. We show that phase is more important than magnitude in determining the structure of a spherical function. We examine the…
By numerical simulations, we show that properly arranged two dimensional periodic arrays, formed by dielectric cylinders embedded in parallel in a uniform medium, can indeed act as an optical lens to focus electromagnetic waves, in…
In this paper, we study hybrid neural representations for spherical data, a domain of increasing relevance in scientific research. In particular, our work focuses on weather and climate data as well as comic microwave background (CMB) data.…
Orbital angular momentum eigenfunctions are readily understood in terms of spherical harmonic wavefunctions. However, the quantum mechanical phenomenon of spin is often said to be mysterious and hard to visualize, with no classical…
Frequency shifts, radiative decay rates, the Ohmic loss contribution to the nonradiative decay rates, fluorescence yields, and photobleaching of a two-level atom radiating anywhere inside or outside a complex spherical nanoshell, i.e. a…