Quasi-Fibonacci oscillators

Abstract

We study the properties of sequences of the energy eigenvalues for some generalizations of q-deformed oscillators including the p,q-oscillator, the 3-, 4- and 5-parameter deformed oscillators given in the literature. It is shown that most of the considered models belong to the class of so-called Fibonacci oscillators for which any three consequtive energy levels satisfy the relation E_{n+1}=λE_n+ρE_{n-1} with real constants λ, ρ. On the other hand, for certain μ-oscillator known from 1993 we prove the fact of its non-Fibonacci nature. Possible generalizations of the three-term Fibonacci relation are discussed among which we choose, as most adequate for the μ$-oscillator, the so-called quasi-Fibonacci (or local Fibonacci) property of the energy levels. The property is encoded in the three-term quasi-Fibonacci (QF) relation with non-constant, n-dependent coefficients λand ρ. Various aspects of the QF relation are elaborated for the μ-oscillator and some of its extensions.

19 pages; v2: few comments and references added; v3: small corrections, to appear in J.Phys.A

References in corpus (8)

• Multi-particle correlations in qp-Bose gas model
• A q-Oscillator with 'Accidental' Degeneracy of Energy Levels
• Generalized Heisenberg Algebras and Fibonacci Series
• Generalized Heisenberg algebras and k-generalized Fibonacci numbers
• Plethora of q-oscillators possessing pairwise energy level degeneracy
• Non-extensive entropy of bosonic Fibonacci oscillators
• A (p,q)-deformed Landau problem in a spherical harmonic well: spectrum and noncommuting coordinates
• Polynomially deformed oscillators as k-bonacci oscillators

Cited by in corpus (6)

• Exact expressions for the intercepts of r-particle momentum correlation functions in μ-Bose gas model
• Three-parameter (two-sided) deformation of Heisenberg algebra
• On the deformed oscillator and the deformed derivative associated with the Tsallis q-exponential
• Hermite polynomials and Fibonacci Oscillators
• New Deformed Heisenberg Algebra from the $\mu$-Deformed Model of Dark Matter
• The $\mu$-deformed Einstein field equations with $\mu$-dependent effective cosmological constant