Related papers: Spin Wavelets on the Sphere
In a previous paper we have introduced a new class of radial basis functions that are powerful means to approximate functions by quasi-interpolation. In this article we extend the results to create new ways of approximating functions by…
We propose a new scheme for numerically computing collective-mode spectra for large-size systems, using a reformulation of the Random Phase Approximation. In this study, we apply this method to investigate the spectrum and nature of the…
{\it Fold maps} are fundamental tools in generalizing the theory of Morse functions and its application to studies of geometric properties of manifolds. One of the fundamental and important problems in the theory of fold maps is to…
In the paper a Riemannian structure on the tangent bundle is defined by using a statistical structure $(g,\nabla)$ on the base manifold. Expressions for various curvatures of the structure are derived. Some rigidity results of the structure…
We give a self-contained and enriched review about topology properties in the rapidly growing field of topological states of matter (TSM). This review is mainly focus on the beautiful interplay of topology mathematics and condensed matter…
We present in this paper new multiscale transforms on the sphere, namely the isotropic undecimated wavelet transform, the pyramidal wavelet transform, the ridgelet transform and the curvelet transform. All of these transforms can be…
We present a new spectral scheme for analysing functions of half-integer spin-weight on the $2$-sphere and demonstrate the stability and convergence properties of our implementation. The dynamical evolution of the Dirac equation on a…
In this PhD Thesis we investigate the geometry of random fields on compact Riemannian manifolds, in particular the two-dimensional sphere. In the first part, we characterize isotropic Gaussian fields on homogeneous spaces of a compact group…
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.…
In this paper, we extend to polarization the method we have recently employed to treat spin. We are led to a generalization of its treatment. Thus, we are able to connect its matrix treatment to first principles, and we obtain the most…
Spin waves offer intriguing novel perspectives for computing and signal processing, since their damping can be lower than the Ohmic losses in conventional CMOS circuits. For controlling the spatial extent and propagation of spin waves on…
We provide a full characterization of the spectral properties of spiral spin density wave (SSDW) states which emerge in one-dimensional electron systems coupled to localized magnetic moments or quantum wires with spin-orbit interactions. We…
Wavelet basis functions are a natural tool for analyzing turbulent flows containing localized coherent structures of different spatial scales. Here, wavelets are used to study the onset and subsequent transition to fully developed…
Due to the emergence of new high resolution numerical weather prediction (NWP) models and the availability of new or more reliable remote sensing data, the importance of efficient spatial verification techniques is growing. Wavelet…
The rich order parameter of Spin Density Waves allows for an unusual object of a complex topological nature: a half-integer dislocation combined with a semi-vortex of the staggered magnetization. It becomes energetically preferable to…
We produce precise estimates for the Kogbetliantz kernel for the approximation of functions on the sphere. Furthermore, we propose and study a new approximation kernel, which has slightly better properties.
Typical LHC analyses search for local features in kinematic distributions. Assumptions about anomalous patterns limit them to a relatively narrow subset of possible signals. Wavelets extract information from an entire distribution and…
Molecular spin clusters are mesoscopic systems whose structural and physical features can be tailored at the synthetic level. Besides, their quantum behavior is directly accessible in laboratory and their magnetic properties can be…
A vortex, a circulating flow around a void, is one of the basic topological phenomena in nature. Here we show that vortices generally emerge in spin wave travelling upon topologically nontrivial magnetic texture, due to the transverse…
We discuss the K\"ahler quantization of moduli spaces of vortices in line bundles over compact surfaces $\Sigma$. This furnishes a semiclassical framework for the study of quantum vortex dynamics in the Schr\"odinger-Chern-Simons model. We…