On the q oscillator and the quantum algebra suq(1,1)

From MaRDI portal
Publication:3491776

DOI10.1088/0305-4470/23/9/003zbMath0709.17012OpenAlexW2012740261MaRDI QIDQ3491776

E. V. Damaskinskiĭ, Petr P. Kulish

Publication date: 1990

Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0305-4470/23/9/003



Related Items

Thermal properties of the \(q\)-deformed spin-one DKP oscillator, CONSTRUCTION OF THE SPECTRAL MEASURE FOR DEFORMED OSCILLATOR POSITION OPERATOR IN THE CASE OF UNDETERMINED HAMBURGER MOMENT PROBLEM, Paragrassmann differential calculus, Orthogonal polynomials and deformed oscillators, The quantum group \(SU_ q(2)\) and \(q\)-analog of angular momentum operators in quantum mechanics, A Rodriguez formula and integration measure for the quantum deformed Legendre functions, New \(q\)-derivative and \(q\)-logarithm, The \(q\)-deformed Cartesian \(\text{osp}(1/2)\) algebra, Qubit Dynamics in a q-Deformed Oscillators Environment, Normal ordering for nonlinear deformed ladder operators and the f-generalization of the Stirling and Bell numbers, The q-boson realization of parametrized cyclic representations of quantum algebras at q p = 1, Tensor operators for quantum groups and applications, The statistical properties of q-deformed Morse potential for some diatomic molecules via Euler-Maclaurin method in one dimension, The algebra of two dimensional generalized Chebyshev-Koornwinder oscillator, Jacobson generators, Fock representations and statistics of sl(n+1), Gauss decomposition for quantum groups and supergroups, Complex analytic realizations for quantum algebras, The statistical properties of the \(q\)-deformed Dirac oscillator in one and two dimensions, More on U q(su(1,1)) with q a root of unity, q-exponential and q-gamma functions. I. q-exponential functionsa), q-exponential and q-gamma functions. II. q-gamma functionsa), Invariant identities in the Heisenberg algebra, Exactly solvable models of quantum nonlinear optics, Correlation functions for a strongly correlated boson system, \(q\)-deformed quadrature operator and optical tomogram, On the deformability of Heisenberg algebras, Quantum inverse scattering method for the \(q\)-boson model and symmetric functions, A simple difference realization of the Heisenberg q-algebra, Boundary value problems for a second-order (p,q)-difference equation with integral conditions, WKB equivalent potentials for q-deformed harmonic and anharmonic oscillators, A q-analog of the quantum central limit theorem for SUq(2), THE RELATIVISTIC OSCILLATOR ALGEBRA REVISITED IN THE QUANTUM GROUPS FORMALISM, Models of q-algebra representations: Tensor products of special unitary and oscillator algebras, \(q\)-oscillator from the \(q\)-Hermite polynomial, Some quantum gate operators for continuum variables in \(q\)-deformed coordinate representation, Even and odd \(q\)-deformed charge coherent states and their nonclassical properties, \(q\)-deformed Barut-Girardello \(\mathrm{su}(1,1)\) coherent states and Schrödinger cat states, Multiboson expansions for the \(q\)-oscillator and \(\text{su}(1,1)_q\), \(q\)-deformed classical mechanics, Connection between \(q\)-deformed anharmonic oscillators and quasi-exactly soluble potentials, Higher moment properties of \(k\)-boson \(q\)-coherent states, Even and odd \(qs\)-coherent states and their photon-statistical properties, Quasi-classical limit in \(q\)-deformed systems, non-commutativity and the \(q\)-path integral., Hopf-type deformed oscillators, their quantum double and a \(q\)-deformed Calogero-Vasiliev algebra., On extended umbral calculus, oscillator-like algebras and generalized Clifford algebra, Compactness property of Lie polynomials in the creation and annihilation operators of the \(q\)-oscillator, Contraction of quantum algebras and \(q\) oscillators, Applications of deformed oscillators, Quantum quenches and generalized Gibbs ensemble in a Bethe Ansatz solvable lattice model of interacting bosons, q-deformed fermion in many-particle systems and its application to BCS theory, Charged Coherent States Related to suq(2) Covariance, Quantum integrability and quantum groups: a special issue in memory of Petr P Kulish, An extension of the Borel-Weil construction to the quantum group \(U_ q(n)\), EXACT SOLVING q DEFORMED BOSON MODEL UNDER OPEN BOUNDARY CONDITION, Calculating statistical distributions from operator relations: The statistical distributions of various intermediate statistics, q-deformed Morse oscillator, Operator realizations of the \(q\)-deformed Heisenberg algebra, Non-relativistic q-gases with low critical temperatures, Combinatorics of a strongly coupled boson system, Zero range process and multi-dimensional random walks, Critical phenomenon of a consistent \(q\)-deformed squeezed state, A realization for the \(q\)-harmonic oscillator, Towards \(\psi\)-extension of Rota's finite operator calculus, On the \(q\)-deformed Dirac oscillator in \((2+1)\)-dimensional space-time, Boson realizations of quantum algebras and some physical spaces with quantum algebra symmetry, Clebsch-Gordan coefficients for the quantum algebra \(su_ q(2)\), Field of sine-Gordon type in spacetime of arbitrary dimension: Existence of the Nelson measure, Solution of the Goursat problem for the Maxwell-Bloch system, Solutions of the Schrödinger equation in the case of a semiinfinite crystal, The semiclassical approximation in quantum mechanics. A new approach, Semiclassical asymptotics for a radial Schrödinger equation with singular potential, Discrete symmetries in quantum scattering, On the quantization of identical particles, Exactly solvable lattice model of rooted branched polymers, Diffusion in layered media at large times, On the wave functions of a covariant linear oscillator, Quantization in the neighborhood of classical solutions in the \(N\) particle problem and superfluidity, Three-scale expansion of the solution of the magnetohydrodynamic equations and the Reynolds equation for a tokamak, A \(q\)-Lorentz algebra from \(q\)-deformed harmonic oscillators, An interacting ensemble of particles in the context of quantum algebra, Generalized discrete \(q\)-Hermite I polynomials and \(q\)-deformed oscillator, Dynamic systems related to the Cremmer-Gervais \(R\)-matrix, Dynamical algebra of the q-deformed three-dimensional oscillator, Tensor operators and Clebsch–Gordan coefficients of the quantum algebra suq(1,1), Q rotations and other Q transformations as unitary nonlinear automorphisms of quantum algebras, Bose–Einstein condensation in a gas of Fibonacci oscillators, Quantum algebra from generalized \(q\)-Hermite polynomials, Representations of the deformed oscillator algebra for different choices of generators, Time-dependent q-deformed bi-coherent states for generalized uncertainty relations, The \(q\)-deformed harmonic oscillator, coherent states, and the uncertainty relation, A Model Which Interpolates Between the Jaynes-Cummings Model and the Buck-Sukumar Model, Quantum algebra as the dynamical symmetry of the deformed Jaynes-Cummings model, Exactly solvable potentials and quantum algebras, Thermostatistics of a q -deformed relativistic ideal Fermi gas, The \(q\)-harmonic oscillator and the Al-Salam and Carlitz polynomials, k -component q-deformed charge coherent states and their nonclassical properties, Deformed quantum harmonic oscillator with diffusion and dissipation, Lindblad master equation for the damped harmonic oscillator with deformed dissipation, Physics of the \(\mathrm{so}_q(4)\) hydrogen atom, Hilbert-Schmidt inner product for an adjoint representation of the quantum algebra \(\overset{\smile}{U}_Q(\mathfrak{SU}_2)\), Quantum repulsive nonlinear Schrödinger models and their ``superconductivity.