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Goce Chadzitaskos

Publications and source records attributed to Goce Chadzitaskos.

8 recordsLinked to original sources
arXiv2022

Asymmetric harmonic oscillator

The solution of one--dimensional asymmetric quantum harmonic oscillator is presented. The asymmetry can be realized, for example, by using two springs, one spring is glued with the mass, and the second spring is freely connected with the mass in the equilibrium point and it is located inside or outside the first spring which acts on the mass only from the contact point on the right. We study the spectrum of a quantum harmonic oscillator, which has a spring constant $ k_-$ to the left of the equilibrium position and a spring constant $ k_ +$ to the right of the equilibrium position. In the presented case the contact point of the second string is the equilibrium point of the first string. The explicit form of eigenfunctions, the way to calculate the eigenvalues and the properties of the eigenfunctions are discussed.

quant-ph↗
arXiv2021

Orthonormal bases on $L^2(\mathbb{R}^+)$

We derive the explicit form of eigenvectors of selfadjoint extension $H_ξ$, parametrized by $ξ\in \langle 0,π),$ of differential expression $ H=-\frac{d^2 }{d x^2} + \frac{x^2 }{4}$ together with the spectrum $σ(H_ξ)$ on the space $L^2(\mathbb{R}^+).$ For each $ξ$ the set of eigenvectors form an orthonormal basis of $L^2(\mathbb{R}^+).$

math.FA↗
arXiv2014

Weyl group orbit functions in image processing

We deal with the Fourier-like analysis of functions on discrete grids in two-dimensional simplexes using $C-$ and $E-$ Weyl group orbit functions. For these cases we present the convolution theorem. We provide an example of application of image processing using the $C-$ functions and the convolutions for spatial filtering of the treated image.

cs.CV↗
arXiv2013

Parabolic Strip Telescope

We present a proposal of a new type of telescopes using a rotating parabolic strip as the primary mirror. It is the most principal modification of the design of telescopes from the times of Galileo and Newton. In order to demonstrate the basic idea, the image of an artificial constellation observed by this kind of telescope was reconstructed using the techniques described in this article. As a working model of this new telescope, we have used an assembly of the primary mirror---a strip of acrylic glass parabolic mirror 40 cm long and 10 cm wid shaped as a parabolic cylinder of focal length 1 m---and an artificial constellation, a set of 5 apertures in a distance of 5 m illuminated from behind. In order to reconstruct the image, we made a series of snaps, each after a rotation of the constellation by 15 degrees. Using Matlab we reconstructed the image of the artificial constellation.

astro-ph.IM↗
arXiv2011

CNOT on Polarization States of Coherent Light

We propose a CNOT gate for quantum computation. The CNOT operation is based on existence of triactive molecules, which in one direction have dipole moment and cause rotation of the polarization plane of linearly polarized light and in perpendicular direction have a magnetic moment. The incoming linearly polarized laser beam is divided into two beams by beam splitter. In one beam a control state is prepared and the other beam is a target. The interaction of polarized states of both beams in a solution containing triactive molecules can be described as interaction of two qubits in CNOT.

quant-ph↗
arXiv2009

Transformation design and nonlinear Hamiltonians

We study a class of nonlinear Hamiltonians, with applications in quantum optics. The interaction terms of these Hamiltonians are generated by taking a linear combination of powers of a simple `beam splitter' Hamiltonian. The entanglement properties of the eigenstates are studied. Finally, we show how to use this class of Hamiltonians to perform special tasks such as conditional state swapping, which can be used to generate optical cat states and to sort photons.

quant-ph↗