Related papers: Squeeze operators in classical scenarios
Motivated by the modeling of three-dimensional fluid turbulence, we define and study a class of stochastic partial differential equations (SPDEs) that are randomly stirred by a spatially smooth and uncorrelated in time forcing term. To…
Circular and hyperbolic fractional-order Fourier transformations are actually Weyl pseudo-differential operators. Their associated kernels and symbols are written explicitly. Products of fractional-order Fourier transformations are obtained…
In this article we explore the quantum properties of a degenerate optical parametric oscillator when it is tuned to the first family of transverse modes at the down converted frequency.
We present a microscopic model of a charge carrier transfer under an action of a constant electric field in a complex medium. Generalizing previous theoretical approaches, we model the dynamical environment hindering the carrier motion by…
We experimentally squeeze the thermal motional state of an optically levitated nanosphere, by fast switching between two trapping frequencies. The measured phase space distribution of our particle shows the typical shape of a squeezed…
We explore the manipulation in phase space of many-body wavefunctions that exhibit self-similar dynamics, under the application of sudden force and/or in the presence of a constant acceleration field. For this purpose, we work out a common…
The first part of the paper is devoted to diffraction phenomena that can be expressed by fractional Fourier transforms whose orders are real numbers. According to a scalar theory, diffraction acts on the amplitude of the electric field as…
We consider the formal prolate spheroid differential operator on a finite symmetric interval and describe all its self-adjoint boundary conditions. Only one of these boundary conditions corresponds to a self-operator differential operator…
Optical tweezers use light from a tightly focused laser beam to manipulate the motion of tiny particles. When the laser light is strongly focused, but still paraxial, its e/m field is characterized by a longitudinal component which is of…
The present work is devoted to the study of fractional powers of vector operators, with particular emphasis on the gradient operator with non-constant coefficients. Within the setting of Clifford algebra $\mathbb{R}_n$, this operator turns…
This paper presents recent results obtained by the authors (partly in collaboration with A. Dabrowska) concerning expansions of zonal functions on Euclidean spheres into spherical harmonics and some applications of such expansions for…
We study polarization squeezing of a pure photon number state which is obviously polarized but the mere change in the basis of polarization leads to simultaneous polarization squeezing in all the components of Stokes operator vector except…
We reveal that classical light diffraction in arrays of specially modulated coupled optical waveguides can simulate the quantum process of two-mode squeezing in nonlinear media, with the waveguide mode amplitudes corresponding the signal…
Differential operators on Schwartz distributions conventionally are defined as the transpose of differential operators on functions with compact support. They do not exhaust all differential operators. We follow algebraic formalism of…
We review the quadratic form of the Laplace operator in 3 dimensions in spehrical coordinates which acts on the transverse components of vector functions. Operators, acting on the parametrizing functions of one of the transverse components…
We consider expanding semiflows on branched surfaces. The family of transfer operators associated to the semiflow is a one-parameter semigroup of operators. The transfer operators may also be viewed as an operator-valued function of time…
Exceptionally elegant formulae exist for the fractional Laplacian operator applied to weighted classical orthogonal polynomials. We utilize these results to construct a solver, based on frame properties, for equations involving the…
The search for spectral shift functions of operators remains an open area of research. In this paper, the Kre\u{\i}n's spectral shift functions are computed for the Lam\'e operator in the Weierstrass form and the Brioschi-Halphen operator…
We put forward an operational degree of polarization that can be extended in a natural way to fields whose wave fronts are not necessarily planar. This measure appears as a distance from a state to the set of all its…
A new $z$-stretching finite difference method is established for simulating the paraxial light beam propagation through a lens in a cylindrically symmetric domain. By introducing proper domain transformations, we solve corresponding…