Related papers: Morlet wavelets in quantum mechanics
This paper develops the use of wavelets as a basis set for the solution of physical problems exhibiting behavior over wide-ranges in length scale. In a simple diagrammatic language, this article reviews both the mathematical underpinnings…
Classical multiscale analysis based on wavelets has a number of successful applications, e.g. in data compression, fast algorithms, and noise removal. Wavelets, however, are adapted to point singularities, and many phenomena in several…
This paper reviews two different uses of the continuous wavelet transform for modal identification purposes. The properties of the wavelet transform, mainly energetic, allow to emphasize or filter the main information within measured…
Recent work introduced a unified framework for steerable and directional wavelets in two and three dimensions that ensures many desirable properties, such as a multi-scale structure, fast transforms, and a flexible angular localization. We…
We construct representations of a q-oscillator algebra by operators on Fock space on positive matrices. They emerge from a multiresolution scaling construction used in wavelet analysis. The representations of the Cuntz Algebra arising from…
We propose a class of spherical wavelet bases for the analysis of geophysical models and forthe tomographic inversion of global seismic data. Its multiresolution character allows for modeling with an effective spatial resolution that varies…
A new representation for solutions of Maxwell's equations is derived. Instead of being expanded in plane waves, the solutions are given as linear superpositions of spherical wavelets dynamically adapted to the Maxwell field and…
I discuss approaches to optimally remove noise from images. A generalization of Wiener filtering to Non-Gaussian distributions and wavelets is described, as well as an approach to measure the errors in the reconstructed images. We argue…
It is demonstrated that the wavelets can be used to considerably speed up simulations of the wave packet propagation in multiscale systems. Extremely high efficiency is obtained in the representation of both bound and continuum states. The…
Geometrical methods in quantum information are very promising for both providing technical tools and intuition into difficult control or optimization problems. Moreover, they are of fundamental importance in connecting pure geometrical…
Warped convolutions of operators were recently introduced in the algebraic framework of quantum physics as a new constructive tool. It is shown here that these convolutions provide isometric representations of Rieffel's strict deformations…
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…
Quantum annealing leverages the properties of interacting quantum spin systems to solve computational problems, typically optimisation problems. Current hardware now has capabilities that can be used to solve condensed matter physics…
In this paper we consider the continuous wavelet transform using Gaussian wavelets multiplied by an appropriate rational term. The zeros and poles of this rational modifier act as free parameters and their choice highly influences the shape…
New elliptic cylindrical wavelets are introduced, which exploit the relationship between analysing filters and Floquet's solution of Mathieu differential equations. It is shown that the transfer function of both multiresolution filters is…
We present a formulation of quantum mechanics based on orthogonal polynomials. The wavefunction is expanded over a complete set of square integrable basis in configuration space where the expansion coefficients are orthogonal polynomials in…
In this paper novel classes of 2-D vector-valued spatial domain wavelets are defined, and their properties given. The wavelets are 2-D generalizations of 1-D analytic wavelets, developed from the Generalized Cauchy-Riemann equations and…
Prompted by the longstanding interpretational controversy in quantum mechanics, quantum tunneling is heuristically addressed within the Everettian quantum multiverse. In this framework, the universal wavefunction splits into decohered…
This work shows the use of a two-dimensional Gabor wavelets in image processing. Convolution with such a two-dimensional wavelet can be separated into two series of one-dimensional ones. The key idea of this work is to utilize a Gabor…
This paper constructs the first quantum algorithm for wavelet packet transforms with a "parabolic scaling" tree structure, sometimes called wave atom transforms. Classically, wave atoms are used to construct sparse representations of…