Applications of deformed oscillators

DOI10.1007/BF01097496zbMath0783.17004MaRDI QIDQ1180110

Petr P. Kulish, E. V. Damaskinskiĭ

Publication date: 27 June 1992

Published in: Journal of Soviet Mathematics (Search for Journal in Brave)

zbMATH Keywords

coherent states\(q\)-oscillatorscontractions of quantum algebrasdeformed Jaynes- Cummings model

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50)

Related Items (17)

Orthogonal polynomials and deformed oscillators ⋮ On the dimensions of oscillator algebras induced by orthogonal polynomials ⋮ The algebra of two dimensional generalized Chebyshev-Koornwinder oscillator ⋮ \(q\)-coherent states associated with the noncommutative complex plane \(\mathbb C_{q^2}\) for the Biedenharn-Macfarlane \(q\)-oscillator ⋮ Color hom-Lie algebras, color hom-Leibniz algebras and color omni-hom-Lie algebras ⋮ Double constructions of biHom-Frobenius algebras ⋮ On classification of \((n+1)\)-dimensional \(n\)-Hom-Lie algebras with nilpotent twisting maps ⋮ On classification of (\(n +1\))-dimensional \(n\)-Hom-Lie algebras for \(n =4,5,6\) and nilpotent twisting map with 2-dimensional kernel ⋮ On \((\lambda,\mu,\gamma)\)-derivations of BiHom-Lie algebras ⋮ Nearly associative and nearly Hom-associative algebras and bialgebras ⋮ On ideals and derived and central descending series of \(n\)-ary Hom-algebras ⋮ Hom-L-R-smash products, Hom-diagonal crossed products and the Drinfeld double of a Hom-Hopf algebra. ⋮ Hom-left-symmetric color dialgebras, Hom-tridendriform color algebras and Yau's twisting generalizations ⋮ Generalized oscillator and its coherent states ⋮ Quasi-Lie structure of \(\sigma \)-derivations of \(\mathbb C[t^{\pm 1}\)] ⋮ Yetter-Drinfeld modules for Hom-bialgebras ⋮ The symmetric q-oscillator algebra: q-coherent states, q-Bargmann–Fock realization and continuous q-Hermite polynomials with 0 < q < 1

Cites Work

• Unnamed Item
• Unnamed Item
• Quantum groups and generalized statistics in integrable models
• Q-analogues of Clifford and Weyl algebras - spinor and oscillator representations of quantum enveloping algebras
• Twisted second quantization
• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• Finite dimensional representations of the quantum analog of the enveloping algebra of a complex simple Lie algebra
• Poisson manifolds and the Schouten bracket
• Twisted \(\text{SU}(2)\) group. An example of a non-commutative differential calculus
• Operatormethoden für q-identitäten
• Self-adjoint phase operator
• Commutators, anti-commutators and Eulerian calculus
• Duality and quantum groups
• The representations of the oscillator group
• q-ANALOGUE OF BOSON COMMUTATOR AND THE QUANTUM GROUPS SU_q(2) AND SU_q(1, 1)
• The covariant linear oscillator and generalized realization of the dynamical SU(1,1) symmetry algebra
• On q-analogues of the quantum harmonic oscillator and the quantum group SU(2)_q
• INTRODUCTION TO THE YANG-BAXTER EQUATION
• The q-deformed boson realisation of the quantum group SU(n)_qand its representations
• q-analogues of the parabose and parafermi oscillators and representations of quantum algebras
• The construction of the q-analogues of the harmonic oscillator operators from ordinary oscillator operators
• On the q oscillator and the quantum algebra su_q(1,1)
• q-analogues of some prototype Berry phase calculations
• Comment on the q-analogues of the harmonic oscillator
• Quantum algebra as the dynamical symmetry of the deformed Jaynes-Cummings model
• Example of infinite statistics
• Hilbert spaces of analytic functions and generalized coherent states
• Canonically Conjugate Pairs, Uncertainty Relations, and Phase Operators
• Do the Equations of Motion Determine the Quantum Mechanical Commutation Relations?

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