Papers by Goce Chadzitaskos
Journal of advances in mathematics and computer science, Dec 11, 2023
In addition to orthogonal polynomials, orthogonal functions also play an important role. Their ap... more In addition to orthogonal polynomials, orthogonal functions also play an important role. Their applications are, among others, in the fields of signal and data analysis, dynamic modeling. They are related to the solution of differential equations. In this paper we derive the explicit form of one parameter family of orthonormal bases on space L 2 (R +). The bases are formed by eigenvectors of the self-adjoint extension H ξ , parametrized by ξ ∈ 0, π), of differential expression H = − d 2 dx 2 + x 2 4 together with the spectrum σ(H ξ) on the space L 2 (R +). For each ξ the set of eigenvectors form an orthonormal basis of L 2 (R +). From the physical point of view, it is a solution of the Schrödinger equation of a harmonic oscillator on a semi-straight line. To correlate platelet count, splenic index (SI), platelet count/spleen diameter ratio and portal-systemic venous collaterals with the presence of esophageal varices in advanced liver disease to validate other screening parameters.
Springer eBooks, 2015
We deal with the Fourier-like analysis of functions on discrete grids in two-dimensional simplexe... more 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.
An Asymmetric Harmonic Oscillator
Trends in mathematics, 2023
Finite-Dimension Al .-PRODUCT
Spectra of Photon Down Conversion
Geometric Methods in Physics, 2009
We demonstrate that quasi-exactly solvable models of quantum mechanics can be used in nonlinear o... more 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 formula is found out.
The two-diffraction system
Optics Communications, 2001
We use the principle of diffraction gratings and the diffraction pattern of two-slit experiments ... more 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.
Journal of Physics A: Mathematical and Theoretical, 2007
Our previous work on quantum kinematics and coherent states over finite configuration spaces is e... more 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 and their overcompleteness proved. Our approach based on geometric symmetry can be used as a kinematic framework for matrix methods in quantum chemistry of ring molecules.
Arxiv preprint arXiv: …, 2008
We consider the problem of quantum state transfer and gate engineering for two-level systems (qub... more We consider the problem of quantum state transfer and gate engineering for two-level systems (qubits) using simple switch control schemes when we cannot implement implement rotations about orthogonal axes due to an unavoidable drift Hamiltonian or ...
Journal of Physics A, May 28, 2009
Our previous work on quantum mechanics in Hilbert spaces of finite dimensions N is applied to elu... more 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 property of the short-time propagator by using a specially devised N × N-approximation of quantum mechanics in L 2 (R) applied to our finite-dimensional analogue of a free quantum particle.
arXiv (Cornell University), Jun 14, 2021
We analyze the possible effect of rings on orbital velocities in galaxies. The superposition of t... more 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, where we show the course of potential curves and the curves of field strength.
International Journal of Theoretical Physics, 1993
The Feynman path integral is constructed for systems whose configuration space is a discrete fini... more 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.
Quantum Mechanics on Z M and q-Deformed Heisenberg-Weyl Algebras
Quantization and Infinite-Dimensional Systems, 1994
The finite-dimensional quantum mechanics yields a more convenient operator basis for representati... more 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.
Cornell University - arXiv, Apr 13, 2022
The solution of one-dimensional asymmetric quantum harmonic oscillator is presented. The asymmetr... more 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.
We propose a CNOT gate for quantum computation. The CNOT operation is based on existence of triac... more 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.
Feynman path integral with underlying noncommutative “geometry” and quantum mechanics in external field
Czechoslovak Journal of Physics, 1992
Noncommutative algebra of translations as a deforming commutative algebra induces a linear vector... more 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 formulation of quantum mechanic.
Orthonormal bases on L^2(ℝ^+)
We derive the explicit form of eigenvectors of selfadjoint extension H_ξ, parametrized by ξ∈⟨ 0,π... more We derive the explicit form of eigenvectors of selfadjoint extension H_ξ, parametrized by ξ∈⟨ 0,π), of differential expression H=-d^2 /d x^2 + x^2 /4 together with the spectrum σ(H_ξ) on the space L^2(ℝ^+). For each ξ the set of eigenvectors form an orthonormal basis of L^2(ℝ^+).
We propose a CNOT gate for quantum computation. The CNOT operation is based on existence of triac... more 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.
Quantization on and coherent states over
Journal of Physics A: Mathematical and General, 1997
Finite-dimensional quantum mechanics (quantum mechanics on finite discrete space - the cyclic gro... more 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.
Journal of Modern Optics, 2009
We study a class of nonlinear Hamiltonians, with applications in quantum optics. The interaction ... more 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.
Three boson interaction process: spectra and coherent states
Journal of Modern Optics, 2013
ABSTRACT We use the methods of constructions of and deformed coherent states in order to construc... more ABSTRACT 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 the Hamiltonian for low number of photons are calculated and the approximation formula is found out. After the discussion on the time evolution and the entanglement, the coherent states are constructed as the eigenstates of the reduced annihilation operator.
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Papers by Goce Chadzitaskos