Papers by C. Daskaloyannis
Nonlinear extension of the u (2) algebra as the symmetry algebra of the planar anisotropic quantum harmonic oscillator with rational ratio of frequencies and``pancake' …
Arxiv preprint nucl-th/ …, 1994
Abstract: The symmetry algebra of the two-dimensional anisotropic quantum harmonic oscillator wit... more Abstract: The symmetry algebra of the two-dimensional anisotropic quantum harmonic oscillator with rational ratio of frequencies, which is characterizing``pancake''nuclei, is identified as a non-linear extension of the u (2) algebra. The finite dimensional ...
The Woods-Saxon Lambda-Nucleus Potential and the Phenomenological Estimate of the Lambda-Well Depth
Lettere Al Nuovo Cimento, 1985
Summary ∧ Woods-Saxon ∧-nucleus potential is considered and an attempt is made for the determina... more Summary ∧ Woods-Saxon ∧-nucleus potential is considered and an attempt is made for the determination of the ∧ well depth and other parameters by leastsquare fitting to experimental binding energies (B ∧) of the ∧ in hypernuclei. The expression for the half-way radius of the well employed is more complicated than the standard onec =r 0∧3/1. The Walecka-type � semi-empirical mass formula � forB ∧, derived by Deloff, is also discussed.
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.
Quadratic algebras for three-dimensional superintegrable systems
Physics of Atomic Nuclei, 2010
Abstract The three-dimensional superintegrable systems with quadratic integrals of motion have fi... more Abstract The three-dimensional superintegrable systems with quadratic integrals of motion have five functionally independent integrals, one among them is the Hamiltonian. Kalnins, Kress, and Miller have proved that in the case of nondegenerate potentials with quadratic integrals of motion there is a sixth quadratic integral, which is linearly independent of the other integrals. The existence of this sixth integral implies that the integrals of motion form a ternary parafermionic-like quadratic Poisson algebra with five generators. In this ...
The algebra of the quantum nondegenerate three-dimensional Kepler-Coulomb potential
Physics of Atomic Nuclei, 2011
Abstract The classical generalized Kepler-Coulomb potential, introduced by Verrier and Evans, cor... more Abstract The classical generalized Kepler-Coulomb potential, introduced by Verrier and Evans, corresponds to a quantum superintegrable system, with quadratic and quartic integrals of motion. In this paper we show that the algebra of the integrals is a quadratic ternary algebra, ie a quadratic extension of a Lie triple system.
Physics of Atomic Nuclei, 2008
The two-dimensional quantum superintegrable systems with quadratic integrals of motion on a manif... more The two-dimensional quantum superintegrable systems with quadratic integrals of motion on a manifold are classified by using the quadratic associative algebra of the integrals of motion. There are six general fundamental classes of quantum superintegrable systems corresponding to the classical ones. Analytic formulas for the involved integrals are calculated in all the cases. All the known quantum superintegrable systems with quadratic integrals are classified as special cases of these six general classes. The coefficients of the quadratic associative algebra of integrals are calculated and they are compared to the coefficients of the corresponding coefficients of the Poisson quadratic algebra of the classical systems. The quantum coefficients are similar to the classical ones multiplied by a quantum coefficient − 2 plus a quantum deformation of order 4 and 6. The systems inside the classes are transformed using St¨ackel transforms in the quantum case as in the classical case. The general form of the St¨ackel transform between superintegrable systems is discussed.
Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 1985
The interaction of charged particles with the alternating electric field inside ferroelectric sub... more The interaction of charged particles with the alternating electric field inside ferroelectric substances is considered in a semiclassical approach. Monoenergetic y-radiation is predicted for relativistic charged particles. The possible applications of this radiation are investigated.
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.
International Journal of Theoretical Physics, 1992
Explicit formulas of all equivalent local potentials for a coupled n-channel problem are calculat... more Explicit formulas of all equivalent local potentials for a coupled n-channel problem are calculated. The general equivalent local potentials constitute a [(~")-1Jcomplex-parameter family of local potentials. For a definite input elastic channel, the uniqueness of the equivalent local potential is shown. The equivalent local potential of the Feshbach optical potential coincides with the equivalent local potential of the n-channel system. The construction of the Feshbach optical potential is a reduction to the dimensionality of the coupled-channel problem, the construction of the equivalent local potential is a diagonalization of the coupled-channel problem, both constructions are compatible manipulations on the set of the coupled-channel system. The properties of the Feshbach optical potential can be used for the study of the properties of the equivalent local potential.
Contribution to the 4th Workshop on Differential Equations and Group Analysis of Integrable systems
Protaras, Cyprus, Oct
Modern Physics Letters A, Sep 21, 1995
Several physical systems (two identical particles in two dimensions, isotropic oscillator and Kep... more Several physical systems (two identical particles in two dimensions, isotropic oscillator and Kepler system in a 2-dim curved space) and mathematical structures (quadratic algebra QH(3), finite W algebraW 0) are shown to posses the structure of a generalized deformed su(2) algebra, the representation theory of which is known. Furthermore, the generalized deformed parafermionic oscillator is identified with the algebra of several physical systems (isotropic oscillator and Kepler system in 2-dim curved space, Fokas-Lagerstrom, Smorodinsky-Winternitz and Holt potentials) and mathematical constructions (generalized deformed su(2) algebra, finite W algebrasW 0 and W (2) 3). The fact that the Holt potential is characterized by the W (2) 3 symmetry is obtained as a by-product.
HNPS Proceedings, 2020
The first realizations of quanttun algebraic symmetries in nuclear and molecular spectra are pres... more The first realizations of quanttun algebraic symmetries in nuclear and molecular spectra are presented. Rotational spectra of even-even nuclei are described by the quantum algebra SUq(2). The two parameter formula given by the algebra is equivalent to an expan- sion in terms of powers of j(j + 1), similar to the expansion given by the Variable Moment of Inertia (VMI) model. The moment of inertia parameter in the two models, as well as the small parameter of the expansion, are found to have very similar numerical values. The same formalism is found to give very good results for superdeformed nuclear bands, which are closer to the classical SU(2) limit, as well as for rotational bands of diatomic molecules, in which a partial summation of the Dunham expansion for rotation-vibration spectra is achieved. Vibrational spectra of diatomic molecules can be described by the q-deformed anhannonic oscillator, having the symmetry Uq(2)>Oq(2). An alternative de- scription is obtained in terms...
HNPS Proceedings, 2020
The explicit formulae of the equivalent local potentials for a coupled channel problem are calcul... more The explicit formulae of the equivalent local potentials for a coupled channel problem are calculated. We prove that the equivalent local potential of the coupled channel system coincides with the equivalent local potential of the Feshbach optical potential.
Universal Quantum Computation with Josephson Junctions
The Physics of Communication - Proceedings of the XXII Solvay Conference on Physics, 2003
Physical Review C, 1982
An investigation is made of the effect of the (central) A-nucleon potential V~and of the density ... more An investigation is made of the effect of the (central) A-nucleon potential V~and of the density distribution p of the a particle on the central part of the V~interaction, in the framework of the rigid-core model, adopted originally in this context by Dalitz and Downs. Single and double Gaussian shapes for V~and p are considered, the latter having the advantage that the charge form factor fits rather well the experimental results deduced from the electron scattering experiments including those at high momentum transfers. The differences observed in the values of Vz depend mainly on the central A-nucleon potential assumed and they are very strong for small values of r. Differences also exist in this region because of the various densities used. The double Gaussian density has the effect of lowering the values of VA near the center of the a particle in almost all the cases of double Gaussian A-nucleon potentials. NUCLEAR STRUCTURE Hypernuclei; qHe; A-a interaction; AN interaction, density of. He.
Physical Review A, 1993
A generalized deformed oscillator giving the same spectrum as the Morse potential is constructed ... more A generalized deformed oscillator giving the same spectrum as the Morse potential is constructed through the use of quantum-algebraic techniques. The model of n coupled anharmonic oscillators of Iachello and Oss [Phys. Rev. Lett. 66, 2976 (1991)],suitable for the description of vibrational spectra of polyatomic molecules, is subsequently written in terms of such generalized deformed oscillators. In addition to clarifying the relation of the model of Iachello and Oss to other models using coupled oscillators for the description of vibrational molecular spectra, the present formalism allows for the construction of a large class of exactly soluble models with no extra computational effort. As an example, the way of including a coupling of the Darling-Dennison type is shown.
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Papers by C. Daskaloyannis