Related papers: A new method to generate superoscillating function…
In this work, we have developed a method to generate ultra-short pulses below the Fourier limit, extending the concept previously worked in reference 1 for generating sub-diffractive Gaussian beams. Alternatively, we introduce new…
The goal of this work is to introduce and study fuzzy limits of functions. Two approaches to fuzzy limits of a function are considered. One is based on the concept of a fuzzy limit of a sequence, while another generalizes the conventional…
We generalize the formalism and the techniques of the supersymmetric (susy) quantum mechanics to the cases where the superpotential is generated/defined by higher excited eigenstates. The generalization is technically almost straightforward…
We present a new interpretation of the terms superposition, entanglement, and measurement that appear in quantum mechanics. We hypothesize that the structure of the wave function for a quantum system at the sub-Planck scale has a…
Fourier transformations of pseudo-Boolean functions are popular tools for analyzing functions of binary sequences. Real-world functions often have structures that manifest in a sparse Fourier transform, and previous works have shown that…
The prolate spheroidal wave functions, which are a special case of the spheroidal wave functions, possess a very surprising and unique property [6]. They are an orthogonal basis of both $L^2(-1,1)$ and the Paley-Wiener space of bandlimited…
We propose an implementation of the algorithm for the fast Fourier transform (FFT) as a quantum circuit consisting of a combination of some quantum gates. In our implementation, a data sequence is expressed by a tensor product of vector…
An oscillatory correlation function has been observed by the coincidence counting of multimode two-photon pairs produced with a degenerate optical parametric oscillator far below threshold. The coherent superposition of the multimode…
Self-sustained oscillators are ubiquitous and essential for metrology, communications, time reference, and geolocation. In its most basic form an oscillator consists of a resonator driven on-resonance, through feedback, to create a periodic…
Ultracold bosons in rotating ring lattices have previously been shown to form macroscopic superpositions of different quasi-momentum states. We demonstrate that the generation of such kind of states using slightly non-uniform ring lattices…
Multicomponent superconductivity is a novel quantum phenomenon in many different superconducting materials, such as multiband ones in which different superconducting gaps open in different Fermi surfaces, films engineered at the atomic…
A class of unitary operations generated by idealized, semiclassical fields is studied. The operations implemented by sharp potential kicks are revisited and the possibility of performing them by softly varying external fields is examined.…
A formula for supershell partition functions, which play a major role in the Super Transition Array approach to radiative-opacity calculations, is derived as a functional of the distribution of energies within the supershell. It consists in…
The concept of quasi-bosons or composite bosons (like mesons, excitons etc.) has a wide range of potential physical applications. Even composed of two pure fermions, the quasi-boson creation and annihilation operators satisfy non-standard…
We propose a novel approach to the generation of electromagnetic oscillations by means of a low-frequency pumping of two coupled linear oscillators. A theory of such generation mechanism is proposed, and its feasibility is demonstrated by…
In this article, we present a space-frequency theory for spherical harmonics based on the spectral decomposition of a particular space-frequency operator. The presented theory is closely linked to the theory of ultraspherical polynomials on…
Optical frequency comb, as a spectrum made of discrete and equally spaced spectral lines, is a light source with essential applications in modern technology. Cavity optomechanical systems were found to be a feasible candidate for realizing…
The full spectrum and eigenfunctions of the quantum version of a nonlinear oscillator defined on an N-dimensional space with nonconstant curvature are rigorously found. Since the underlying curved space generates a position-dependent…
In this paper maximal commutators and commutators of maximal functions with functions of bounded mean oscillation are investigated. New pointwise estimates for them are proved.
We identify a broad class of physical processes in an optical quantum circuit that can be efficiently simulated on a classical computer: this class includes unitary transformations, amplification, noise, and measurements. This…