Related papers: p-Adic wavelet transform and quantum physics
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…
We recently introduced the Alchemical Integral Transform (AIT) enabling the prediction of energy differences, and guessed an Ansatz to parametrize space $\pmb{r}$ in some alchemical change $\lambda$. Here, we present a rigorous derivation…
We introduce the notion of $p$-adic quantum bit ($p$-qubit) in the context of the $p$-adic quantum mechanics initiated and developed by Volovich and his followers. In this approach, physics takes place in three-dimensional $p$-adic space…
The quantum quartic oscillator is investigated in order to test the many-body technique of the continuous unitary transformations. The quartic oscillator is sufficiently simple to allow a detailed study and comparison of various…
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…
The empirical wavelet transform is an adaptive multiresolution analysis tool based on the idea of building filters on a data-driven partition of the Fourier domain. However, existing 2D extensions are constrained by the shape of the…
Examples are given of q-deformed systems that may be interpreted by the standard rules of quantum theory in terms of new degrees of freedom and supplementary quantum numbers.
A brief review of the previous research on the Heisenberg uncertainty relations at the Planck scale is given. In this work, investigation of the uncertainty principle extends to p-adic and adelic quantum mechanics. In particular, p-adic…
The Quantum Fourier Transform offers an interesting way to perform arithmetic operations on a quantum computer. We review existing Quantum Fourier Transform adders and multipliers and propose some modifications that extend their…
This paper produces various results on $p$-adic multiframelet. Multiframelet is a frame-like sequence generated by multiple functions along with wavelet structure. Various properties of multiframelet in $L^{2}(\mathbb{Q}_{p})$ have been…
Different techniques to speed up quantum adiabatic processes are currently being explored for applications in atomic, molecular and optical physics, such as transport, cooling and expansions, wavepacket splitting, or internal state control.…
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…
A quantum bit encoding converter between qubits of different forms is experimentally demonstrated, paving the way to efficient networks for optical quantum computing and communication.
Space-time light structuring has emerged as a very powerful tool for controlling the propagation dynamics of pulsed beam. The ability to manipulate and generate space-time distributions of light has been remarkably enhanced in past few…
We propose and study a quantum pump which emulates a traditional paddlewheel, that can be implemented with ultracold atoms in waveguides. We use wavepacket propagation to study its single-mode dynamics, which also determines its multimode…
The possibility of a quantum system to exhibit properties that are akin to both the classically held notions of being a particle and a wave, is one of the most intriguing aspects of the quantum description of nature. These aspects have been…
Wavelet analysis and compression tools are reviewed and different applications to study MHD and plasma turbulence are presented. We introduce the continuous and the orthogonal wavelet transform and detail several statistical diagnostics…
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,…
Adelic quantum mechanics is form invariant under an interchange of real and p-adic number fields as well as rings of p-adic integers. We also show that in adelic quantum mechanics Feynman's path integrals for quadratic actions with rational…
The past decade has seen atomic Bose-Einstein condensates emerge as a promising prototype system to explore the quantum mechanical form of turbulence, buoyed by a powerful experimental toolbox to control and manipulate the fluid, and the…