Related papers: The wave packet propagation using wavelets
In this article, we investigate the application of wavelet packet transform as a novel spectrum sensing approach. The main attraction for wavelet packets is the tradeoffs they offer in terms of satisfying various performance metrics such as…
We show how periodized wavelet packet transforms and periodized wavelet transforms can be implemented on a quantum computer. Surprisingly, we find that the implementation of wavelet packet transforms is less costly than the implementation…
Wavelet transforms are widely used in various fields of science and engineering as a mathematical tool with features that reveal information ignored by the Fourier transform. Unlike the Fourier transform, which is unique, a wavelet…
We draw attention to various aspects of number theory emerging in the time evolution of elementary quantum systems with quadratic phases. Such model systems can be realized in actual experiments. Our analysis paves the way to a new,…
Different kinds of wave packet transforms are widely used for extracting multi-scale structures in signal processing tasks. This paper introduces the quantum circuit implementation of a broad class of wave packets, including Gabor atoms and…
The notion of wavelets is defined. It is briefly described {\it what} are wavelets, {\it how} to use them, {\it when} we do need them, {\it why} they are preferred and {\it where} they have been applied. Then one proceeds to the…
New experimental techniques based on non-linear ultrafast spectroscopies have been developed over the last few years, and have been demonstrated to provide powerful probes of quantum dynamics in different types of molecular aggregates,…
In this paper, we use a straightforward numerical method to solve scattering models in one-dimensional lattices based on a tight-binding band structure. We do this by using the wave packet approach to scattering, which presents a more…
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…
In the general context of complex data processing, this paper reviews a recent practical approach to the continuous wavelet formalism on the sphere. This formalism notably yields a correspondence principle which relates wavelets on the…
The study addresses the quantum spreading of a localized stationary flow of high energy particles. Results demonstrate that as particle energy increases, the spreading speed of the particle wave packet diminishes rapidly. Concurrently,…
We study the use of the quantum wavelet transform to extract efficiently information about the multifractal exponents for multifractal quantum states. We show that, combined with quantum simulation algorithms, it enables to build quantum…
A non-dispersing wave packet has been attracting much interest from various scientific and technological viewpoints. However, most quantum systems are accompanied by anharmonicity, so that retardation of quantum wave-packet dispersion is…
Wavelet based algorithms in numerical analysis are similar to other transform methods in that vectors and operators are expanded into a basis and the computations take place in this new system of coordinates. However, due to the recursive…
Multi-scale wave propagation problems are computationally costly to solve by traditional techniques because the smallest scales must be represented over a domain determined by the largest scales of the problem. We have developed and…
A wave packet undergoes a strong spatial and temporal dispersion while propagating through a complex medium. This wave scattering is often seen as a nightmare in wave physics whether it be for focusing, imaging or communication purposes.…
Waves in excitable media can be treated by a simple geometric theory. The propagation velocity is assumed known and evolution of wave fronts is determined by elementary physical principles (Fermat's principle, Huygens' principle). Based on…
Quantum computing provides a novel avenue towards simulating dynamical phenomena, and, in particular, scattering processes relevant for exploring the structure of matter. However, preparing and evolving particle wave packets on a quantum…
We propose an implementation of the quantum fast Fourier transform algorithm in an entangled system of multilevel atoms. The Fourier transform occurs naturally in the unitary time evolution of energy eigenstates and is used to define an…
In this paper, we study the synthesis of Gegenbauer processes using the wavelet packets transform. In order to simulate a 1-factor Gegenbauer process, we introduce an original algorithm, inspired by the one proposed by Coifman and…