# Goce ChadzitaskosCzech Technical University in Prague | ČVUT

Goce Chadzitaskos

## About

39

Publications

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108

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## Publications

Publications (39)

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 f...

We analyze the possible effect of rings on orbital velocities in galaxies. The superposition of the central force with the gravitational forces induced by the rings opens up various possibilities of the course of orbital velocities. The orbital velocity depends on the position of the star in the ring. We illustrate this dependence on several models...

Explicit form of eigenvectors of selfadjoint extension $H_\xi$, parametrized by $\xi \in \langle 0,\pi),$ of differential expression $ H=-\frac{d^2 }{d x^2} + \frac{x^2 }{4}$ considered on the space $L^2(\mathbb R^+)$ are derived together with spectrum $\sigma(H_\xi).$ For each $\xi$ the set of eigenvectors form orthonormal basis of $L^2(\mathbb R^...

The study of the evolution process of our visual system indicates the existence of variational spatial arrangement; from densely hexagonal in the fovea to a sparse circular structure in the peripheral retina. Today’s sensor spatial arrangement is inspired by our visual system. However, we have not come further than rigid rectangular and, on a minor...

The study of the evolution process of our visual system indicates the existence of variational spatial arrangement; from densely hexagonal in the fovea to a sparse circular structure in the peripheral retina. [...]

We are considering polytopes with exact reflection symmetry group G in the real 3-dimensional Euclidean spaceR3. By changingone simple element of the polytope (position of one vertex or length of an edge), one canretain the exact symmetry of the polytope by simultaneously changing other correspondingelements of the polytope. A simple method of usin...

This paper presents an innovative telescope design based on the usage of a parabolic strip fulfilling the function of an objective. Isaac Newton was the first to solve the problem of chromatic aberration, which is caused by a difference in the refractive index of lenses. This problem was solved by a new kind of telescope with a mirror used as an ob...

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.

We present the first attempt to use the C-orbit functions in image processing. For the image processing we perform a Fourier-like transform of the image. Then we define a convolution on C-orbit functions and we apply the simplest spatial linear filters on several examples. Finally we compare the results with filtering via an ordinary Fourier transf...

About 60 years ago, I. Shmushkevich presented a simple ingenious method for computing the relative probabilities of channels involving the same interacting multiplets of particles, without the need to compute the Clebsch-Gordan coefficients. The basic idea of Shmushkevich is “isotopic non-polarization” of the states before the interaction and after...

A overview of our patented proposals of new optical elements is presented. The elements are suitable for laser pulse analysis, telescopy, X-ray microscopy and X-ray telescopy. They are based on the interference properties of light: a special grating for a double slit pattern, parabolic strip imaging for a telescope, and Bragg’s condition for X-ray...

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...

We use the methods of constructions of and deformed coherent states in order to construct the coherent states for down conversion processes. The down conversion process can be understood as a quasi-exactly solvable model of quantum mechanics. After the reduction of the Hamiltonian, we use the Turbiner polynomials approach, and the eigenvalues of th...

We present a possible construction of coherent states on the unit circle as configuration space. Our approach is based on Borel quantizations on S¹ including the Aharonov–Bohm-type quantum description. Coherent states are constructed by Perelomov's method as group-related coherent states generated by Weyl operators on the quantum phase space . Beca...

A theory of grading preserving contractions of representations of Lie algebras has been developed. In this theory, grading of the given Lie algebra is characterized by two sets of parameters satisfying a derived set of equations. Here we introduce a list of resulting 3-dimensional representations for the Z{double struck} 3-grading of the sl(2) Lie...

A theory of grading preserving contractions of representations of Lie algebras has been developed. In this theory, grading of the given Lie algebra is characterized by two sets of parameters satisfying a derived set of equations. Here we introduce a list of resulting 3-dimensional representations for the Z3-grading of the sl(2) Lie algebra.

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 beam...

We present a possible construction of coherent states on the unit circle
as configuration space. In our approach the phase space is the product
ℤ×S1. Because of the duality of canonical coordinates
and momenta, i.e. the angular variable and the integers, this
formulation can also be interpreted as coherent states over an infinite
periodic chain. Fo...

We demonstrate that quasi-exactly solvable models of quantum mechanics can be used in nonlinear optical processes for a down conversion or second-harmonic generation processes. After the reduction we use the Turbiner and Bender -Dunne polynomial approach. The eigenvalues of Hamiltonian for low number of photons are calculated and the approximation...

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 spe...

Our previous work on quantum mechanics in Hilbert spaces of finite dimensions N is applied to elucidate the deep meaning of Feynman's path integral pointed out by G. Svetlichny. He speculated that the secret of the Feynman path integral may lie in the property of mutual unbiasedness of temporally proximal bases. We confirm the corresponding propert...

We present a proposal for a X-ray optical element suitable for X-ray microscopy and other X-ray-based display systems. Its principle is based on the Fresnel lenses condition and the Bragg condition for X-ray scattering on a slice of monocrystal. These conditions are fulfilled simultaneously due to a properly machined shape of the monocrystal with a...

An explicit algorithm for calculating the optimized Euler angles for both qubit state transfer and gate engineering given two arbitary fixed Hamiltonians is presented. It is shown how the algorithm enables us to efficiently implement single qubit gates even if the control is severely restricted and the experimentally accessible Hamiltonians are far...

The construction of coherent states for an open finite chains comes from q-deformed harmonic oscillator when q is the (M+1)th root of the unity [3]. We modify this approach and construct such coherent states, using para-Grassmann variables over M dimensional complex space CM. We show that the integration of the reproducing kernel in [1] can be real...

We present exact solutions for two nonlinear models each of which
describes parametric down conversion of photons as well as the Kerr
effect. The Hamiltonians for these models are related to the dual Hahn
finite orthogonal polynomials. Explicit expressions are obtained for the
spectra and for the eigenvectors of the Hamiltonians. A discussion of
th...

Our previous work on quantum kinematics and coherent states over finite configuration spaces is extended: the configuration space is, as before, the cyclic group Z_n of arbitrary order n=2,3,..., but a larger group - the non-Abelian dihedral group D_n - is taken as its symmetry group. The corresponding group related coherent states are constructed...

We present exact solutions of a class of models, which describe the parametric down conversion of photons. The Hamiltonians of this models are related to the classes of finite orthogonal polynomials. The spectra and explicit expressions for eigenvectors of this Hamiltonians are obtained. Comment: 12 pages, some corrections and chapter added

We construct a deformation quantization for two cases of configuration spaces: the multiplicative group of positive real numbers R + and the circle S 1 . In these cases we define the momenta using the Fourier transform. Using the identification of symbols of quantum observables — real functions on the phase space — with classical observables, we in...

The eigenproblem for a class of Hamiltonians of the parametric down conversion process in the Kerr medium is solved. Some physical characteristics of the system are calculated.

The angular resolution is tha ability of a telescope to render detail: the higher the resolution the finer is the detail. it is, together with the aperture, the most important characteristic of telescopes. We propose a new construction of telescopes with improved ratio of angular resolution and area of the primary optical element (mirror or lense)....

We use the principle of diffraction gratings and the diffraction pattern of two-slit experiments in construction of a two-diffraction system. The two-diffraction system is a candidate for secure information exchange, and it is suitable for using in optical experiments including two-photon state experiments.

Finite-dimensional quantum mechanics (quantum mechanics on finite discrete space - the cyclic group of order M) is developed further: in analogy with the usual harmonic oscillator coherent states, an overcomplete family of coherent states over the phase space is constructed and their properties are determined.

In this Letter, we construct the star product for polynomials over the para-Grassmann variable and we present as an example a para-Grassmann version of the model of q–quantum mechanics. Moreover, using the structural relations of the q–deformed algebra generated by annihilation and creation operators, we decompose the Jacobi matrix in the product o...

*-product formulation of finite-dimensional quantum mechanics introduces an other multiplication law between square real matrices (which play a role of classical observables on discrete phase space). Then the analogy of classical mechanics on discrete space is done by multiplication law where the element of resulting matrix is the product of corres...

The finite-dimensional quantum mechanics yields a more convenient operator basis for representation of q-deformed Heisenberg-Weyl (q-HW) algebras when q is a root of unity, i.e. q
M
= 1. Two free parameters appear when the representation is constructed. Moreover, the irreducibility of the representations is discussed.

The Feynman path integral is constructed for systems whose configuration space is a discrete finite set. The construction is based on the operator formulation of quantum mechanics on a finite discrete space. We derive connections between operators and introduce the analogue of the*-multiplication for discrete symbols.

Noncommutative algebra of translations as a deforming commutative algebra induces a linear vector potential in the plane. This potential perturbs the generators of translations. Such potential we can identify, for example, with constant magnetic or with homogeneous electric fields. This potential introduces an extra phase factor in the Feynman form...