Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/11351
Title: Quantum calculus of Fibonacci divisors and infinite hierarchy of Bosonic-Fermionic Golden quantum oscillators
Authors: Pashaev, Oktay
Keywords: Fibonacci numbers
Fibonacci divisors
Golden ratio
Quantum oscillators
Coherent states
Quantum calculus
Golden analytic functions
Publisher: World Scientific Publishing
Abstract: Starting from divisibility problem for Fibonacci numbers, we introduce Fibonacci divisors, related hierarchy of Golden derivatives in powers of the Golden Ratio and develop corresponding quantum calculus. By this calculus, the infinite hierarchy of Golden quantum oscillators with integer spectrum determined by Fibonacci divisors, the hierarchy of Golden coherent states and related Fock-Bargman representations in space of complex analytic functions are derived. It is shown that Fibonacci divisors with even and odd kappa describe Golden deformed bosonic and fermionic quantum oscillators, correspondingly. By the set of translation operators we find the hierarchy of Golden binomials and related Golden analytic functions, conjugate to Fibonacci number F-kappa. In the limit. kappa -> 0, Golden analytic functions reduce to classical holomorphic functions and quantum calculus of Fibonacci divisors to the usual one. Several applications of the calculus to quantum deformation of bosonic and fermionic oscillator algebras, R-matrices, geometry of hydrodynamic images and quantum computations are discussed.
URI: https://doi.org/10.1142/S0219887821500754
https://hdl.handle.net/11147/11351
ISSN: 0219-8878
1793-6977
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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