Related papers: Unusual Properties of Superoscillating Particles
We further develop the concept of supergrowth [Jordan, Quantum Stud.: Math. Found. $\textbf{7}$, 285-292 (2020)], a phenomenon complementary to superoscillation, defined as the local amplitude growth rate of a function being higher than its…
We investigate the influence of superpositional wave function oscillations on the performance of Shor's quantum algorithm for factorization of integers. It is shown that the wave function oscillations can destroy the required quantum…
Quantum transients are temporary features of matter waves before they reach a stationary regime. Transients may arise after the preparation of an unstable initial state or due to a sudden interaction or a change in the boundary conditions.…
Superoscillation is a counterintuitive phenomenon for its mathematical feature of ``faster-than-Fourier", which has allowed novel optical imaging beyond the diffraction limit. In this article, we introduce a superoscillating quantum control…
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…
M.V. Berry's work [J. Phys. A: Math. Theor. 43, 415302 (2010)] highlighted the correspondence between backflow in quantum mechanics and superoscillations in waves. Superoscillations refer to situations where the local oscillation of a…
Special relativity combined with the stochastic vacuum flux impact model lead to an explicit interpretation of many of the phenomena of elementary quantum mechanics. We examine characteristics of a repetitively impacted submicroscopic…
The wave function was proposed for description of quantum phenomena on the atomic level. But now it is well known that quantum phenomena are observed not only on atomic level and the wave function is used for description of macroscopic…
Supersymmetric ground state wave functions of a model of supersymmetric quantum mechanics on $S^1$ (supersymmetric simple pendulum) are studied. Supersymmetry can be broken due to the existence of an undetermined parameter, which is…
The concept of superbandwidth refers to the fact that a band-limited signal can exhibit, locally, an increase of its bandwidth, i.e., an effective bandwidth greater than that predicted by its Fourier transform. In this work, we study the…
In this paper we use techniques in Fock spaces theory and compute how the Segal-Bargmann transform acts on special wave functions obtained by multiplying superoscillating sequences with normalized Hermite functions. It turns out that these…
Quantum-classical correspondence for the average shape of eigenfunctions and the local spectral density of states are well-known facts. In this paper, the fluctuations that quantum mechanical wave functions present around the classical…
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 report a method for constructing bandpass functions that approximate a given analytic function with arbitrary accuracy over a finite interval. A corollary is that bandpass functions can be obtained that oscillate arbitrarily slower than…
We consider the superposition of plane waves and localized wave packets. This kind of wave function can result from a local excitation of a particle described by a plane wave. For charged particles, the wave packet means a current, the time…
We give an explicit formula, as a formal differential operator, for quantum microformal morphisms of (super)manifolds that we introduced earlier. Such quantum microformal morphisms are essentially oscillatory integral operators or Fourier…
Arguments from scale physics, augmented by numerical and analytical investigations, are used to consider the probability and the detectability of superoscillations in generic functions. The detectability is defined as the fraction of the…
This is a non-technical presentation (in historical context) of the quantum theory that is strictly based on global unitarity. While the first part was written for a general readership, Sect. 5 may appear a bit provocative. I argue that the…
Superoscillation (SO) wavefunctions, that locally oscillate much faster than its fastest Fourier component, in light waves have enhanced optical technologies beyond diffraction limits, but never been controlled into 2D periodic lattices.…
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…