Related papers: New methods for creating superoscillations
Quantum computing exploits the quantum-mechanical nature of matter to exist in multiple possible states simultaneously. This new approach promises to revolutionize the present form of computing. As an approach to quantum computing, we…
A mixed supersymmetric-algebraic approach to construction of the minimum uncertainty coherent states of anharmonic oscillators is presented. It permits generating not only the well-known coherent states of the harmonic and Morse oscillators…
We investigate symmetric oscillators, and in particular their quantization, by employing semiclassical and quantum phase functions introduced in the context of Liouville-Green transformations of the Schr\"{o}dinger equation. For anharmonic…
Discovered by us [1] special (permanent) resonance mechanism of spectral zone creation in periodic structures is generalized to the case of discrete space lattices and finite difference Schroedinger equation with local V(n) and minimally…
Many systems in physics, chemistry and biology exhibit oscillations with a pronounced random component. Such stochastic oscillations can emerge via different mechanisms, for example linear dynamics of a stable focus with fluctuations,…
Fourier extension is an approximation method that alleviates the periodicity requirements of Fourier series and avoids the Gibbs phenomenon when approximating functions. We describe a similar extension approach using regular wavelet bases…
This paper explains existing results for the application of special functions to phase estimation, which is a fundamental topic in quantum information. We focus on two special functions. One is prolate spheroidal wave function, which…
Over the last two decades, following the early developments on maximally localized Wannier functions, an ecosystem of electronic-structure simulation techniques and software packages leveraging the Wannier representation has flourished.…
We present a new method for the generation of atmospheric turbulence phase screens based on the frequency shift property of the Fourier transform. This method produces low spatial frequency distortions without additional computation time…
In phase space, we analytically obtain the characteristic functions (CFs) of a forced harmonic oscillator [Talkner et al., Phys. Rev. E, 75, 050102 (2007)], a time-dependent mass and frequency harmonic oscillator [Deffner and Lutz, Phys.…
We construct solutions to the eikonal equation for a class of long-range potentials, derive strong radiation condition bounds for the corresponding Schr\"odinger operator and apply them to construct the generalized Fourier transform,…
After reviewing some experimental facts, and early theories, I sketch the Hartree-Fock description of Boson solids, emphasizing the contrast with the Fermion case in that the natural solution is a product of local wave-functions. I then…
We present a user-friendly and versatile experimental technique that generates sub-kilohertz sinusoidal oscillatory flows within microchannels. The method involves the direct interfacing of microfluidic tubing with a loudspeaker diaphragm…
We present a method to synthesize phase screens for multi-wavelength, atmospheric wave optics simulations using fast Fourier transforms. We validate our work by comparing the theoretical, two-wavelength optical path length structure…
Approximate $p$-point Leibniz derivation formulas as well as interpolatory Simpson quadrature sums adapted to oscillatory functions are discussed. Both theoretical considerations and numerical evidence concerning the dependence of the…
In view of recently demonstrated joint use of novel Fourier-transform techniques and effective high-accuracy frequency domain solvers related to the Method of Moments, it is argued that a set of transformative innovations could be developed…
Planar flows with a free boundary in a partially filled and nonuniformly rotating container, with a strongly noncircular shape of the cross-section, are investigated numerically within the ideal fluid approximation. Vorticity is assumed…
A set of exactly computable orthonormal basis functions that are useful in computations involving constituent quarks is presented. These basis functions are distinguished by the property that they fall off algebraically in momentum space…
Quantum sensing and quantum information processing use quantum advantages such as squeezed states that encode a quantity of interest with higher precision and generate quantum correlations to outperform classical methods. In harmonic…
In this paper, we study functional approximations where we choose the so-called radial basis function method and more specifically, quasi-interpolation. From the various available approaches to the latter, we form new quasi-Lagrange…