Related papers: New methods for creating superoscillations
In this work, we propose a new three-dimensional nonlocal spinor superfield model. This theory is constructed by introducing form factors in the local spinor superfield action. Then, we couple it minimally to a scalar superfield, for which…
We prove upper bounds on the number of resonances and eigenvalues of Schr\"odinger operators $-\Delta+V$ with complex-valued potentials, where $d\geq 3$ is odd. The novel feature of our upper bounds is that they are \emph{effective}, in the…
A Fourier transform method is introduced for a class of hybrid time-frequency methods that solve the acoustic scattering problem in regimes where the solution exhibits both highly oscillatory behavior and slow decay in time. This extends…
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…
Superscattering, i.e., a phenomenon of the scattering cross section from a subwavelength object exceeding the single-channel limit, has important prospects in enhanced sensing/spectroscopy, solar cells, and biomedical imaging.…
Extensions of the split-step Fourier method (SSFM) for Schr\"odinger-type pulse propagation equations for simulating femto-second pulses in single- and two-mode optical communication fibers are developed and tested for Gaussian pulses. The…
Hypergeometric functions and their generalizations play an important r\^{o}les in diverse applications. Many authors have been established generalizations of hypergeometric functions by a number ways. In this paper, we aim at establishing…
We consider non oscillatory functions and prove an everywhere Fourier Inversion Theorem for functions of very moderate decrease. The proofs rely on some ideas in nonstandard analysis.
In this paper, we introduce an algorithm that provides approximate solutions to semi-linear ordinary differential equations with highly oscillatory solutions, which, after an appropriate change of variables, can be rewritten as…
Superoscillating functions and supershifts appear naturally in weak measurements in physics. Their evolution as initial conditions in the time dependent Schr\"odinger equation is an important and challenging problem in quantum mechanics and…
A set of semi-analytical techniques based on Fourier analysis is used to solve wave scattering problems in variously shaped waveguides with varying normal admittance boundary conditions. Key components are newly developed conformal mapping…
We develop two classes of composite moment-free numerical quadratures for computing highly oscillatory integrals having integrable singularities and stationary points. The first class of the quadrature rules has a polynomial order of…
Mesoscopic quantum superpositions, or Schr\"odinger cat states, are widely studied for fundamental investigations of quantum measurement and decoherence as well as applications in sensing and quantum information science. The generation and…
Covariance functions and variograms play a fundamental role in exploratory analysis and statistical modelling of spatial and spatio-temporal datasets. In this paper, we construct a new class of spatial covariance functions using the Fourier…
This paper presents a novel boundary-optimized fast Fourier extension algorithm for efficient approximation of non-periodic functions. The proposed methodology constructs periodic extensions through strategic utilization of boundary…
Quasi-two-dimensional superconductors with tunable spin-orbit coupling are very interesting systems with properties that are also potentially useful for applications. In this manuscript we demonstrate that these systems exhibit undamped…
After introducing Schr\"odinger equation within position- dependent mass formalism, a quasi-oscillator has been considered. Eigen functions and energy spectra have been obtained analytical. Then thermodynamic properties, information entropy…
We propose a simple quantum algorithm for simulating highly oscillatory quantum dynamics, which does not require complicated quantum control logic for handling time-ordering operators. To our knowledge, this is the first quantum algorithm…
In this paper, we define a new type multivariable hypergeometric function. Then, we obtain some generating functions for these functions. Furthermore, we derive various families of multilinear and multilateral generating functions for these…
We show that a grating amplitude stationary in space but oscillating in time can be accurately modelled as a set of independent gratings travelling in opposite directions, interacting almost exclusively with waves travelling in the same…