Related papers: Squeeze operators in classical scenarios
This paper presents some properties and applications of "transversal operators". Two transversal operators are presented: a "translation" operator T and a "dilation" operator D. Such operators are used in common analysis systems including…
Classical prolate spheroidal functions play an important role in the study of time-band limiting, scaling limits of random matrices, and the distribution of the zeros of the Riemann zeta function. We establish an intrinsic relationship…
The fractional Fourier transform (FrFT), a fundamental operation in physics that corresponds to a rotation of phase space by any angle, is also an indispensable tool employed in digital signal processing for noise reduction. Processing of…
We investigate the skew-adjoint extensions of a partial derivative operator acting in the direction of one of the sides a unit square. We investigate the unitary equivalence of such extensions and the spectra of such extensions. It follows…
We generalize the generalized-squeezing problem to include fractional values of the squeezing order $n$. This approach allows us to determine the locations of critical points at which qualitative changes in behaviour occur and accurately…
We study the dynamics of classical and quantum particles with spin and dipole moments in external fields within the framework of the general approach by making use of the projection technique. Applications include the neutrino physics in…
For $\alpha\geq 2$, we investigate a class of Fourier extension operators on fractional surfaces $(\xi,|\xi|^\alpha)$. For the corresponding $\alpha$-Strichartz inequalities, by applying the missing mass method and bilinear restriction…
We study wave propagation in periodic and frequency dependent materials. The approach in this paper leads to spectral analysis of a quadratic operator pencil where the spectral parameter relates to the quasimomentum and the frequency is a…
Fractional calculus has been used to describe physical systems with complexity. Here, we show that a fractional calculus approach can restore or include complexity in any physical systems that can be described by partial differential…
We obtain a characterisation of the Fourier transform on the space of Schwartz class functions on $\mathbb{R}^n.$ The result states that any appropriately additive bijection of the Schwartz space onto itself, which interchanges convolution…
Unbound wave packets propagating to macroscopic space and time coordinates become proportional to their (Fourier transform) momentum distribution at earlier times whereby the asymptotic coordinates and the initial momenta are connected…
A form of the Laplace transform is reviewed as a paradigm for an entire class of fractional functional transforms. Various of its properties are discussed. Such transformations should be useful in application to differential/integral…
The Gibbs phenomenon is widely known for Fourier expansions of periodic functions and refers to the phenomenon that the $n$th Fourier partial sums overshoot a target function at jump discontinuities in such a way that such overshoots do not…
A technique is presented for finding the classical Lagrange function corresponding to a given dispersion relation. This allows us to study the classical analogue of the Standard-Model Extension. Developments are discussed.
We propose a source of multimode squeezed light that can be used for the superresolving microscopy beyond the standard quantum limit. This source is an optical parametric amplifier with a properly chosen diaphragm on its output and a…
Classical geometric and topological operations on polyhedra, maps and polytopes often give rise to structures with the same symmetry group as the original one, but with more flags. In this paper we introduce the notion of voltage operations…
We review some aspects of the theory of spherical Bessel functions and Struve functions by means of an operational procedure essentially of umbral nature, capable of providing the straightforward evaluation of their definite integrals and…
We propose a novel method for constructing wavelet transforms of functions defined on the vertices of an arbitrary finite weighted graph. Our approach is based on defining scaling using the the graph analogue of the Fourier domain, namely…
This contribution has two main purposes. First, we show using classical optics how to model two coupled quantum harmonic oscillators and two interacting quantized fields. Second, we use quantum mechanical techniques to solve, exactly, the…
We address the dynamics of a qubit interacting with a quasi static random classical field having both a longitudinal and a transverse component and described by a Gaussian stochastic process. In particular, we analyze in details the…