Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/11351
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dc.contributor.authorPashaev, Oktay-
dc.date.accessioned2021-11-06T09:46:58Z-
dc.date.available2021-11-06T09:46:58Z-
dc.date.issued2021-
dc.identifier.issn0219-8878-
dc.identifier.issn1793-6977-
dc.identifier.urihttps://doi.org/10.1142/S0219887821500754-
dc.identifier.urihttps://hdl.handle.net/11147/11351-
dc.description.abstractStarting 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.en_US
dc.description.sponsorshipTUBITAKTurkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK) [116F206]en_US
dc.description.sponsorshipThis paper is dedicated to the memory of my father on the occasion of his 100th birthday. The work was supported by TUBITAK Grant 116F206.en_US
dc.language.isoenen_US
dc.publisherWorld Scientific Publishingen_US
dc.relation.ispartofInternational Journal of Geometric Methods in Modern Physicsen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectFibonacci numbersen_US
dc.subjectFibonacci divisorsen_US
dc.subjectGolden ratioen_US
dc.subjectQuantum oscillatorsen_US
dc.subjectCoherent statesen_US
dc.subjectQuantum calculusen_US
dc.subjectGolden analytic functionsen_US
dc.titleQuantum calculus of Fibonacci divisors and infinite hierarchy of Bosonic-Fermionic Golden quantum oscillatorsen_US
dc.typeArticleen_US
dc.authorid0000-0002-6249-1277-
dc.institutionauthorPashaev, Oktay-
dc.departmentİzmir Institute of Technology. Mathematicsen_US
dc.identifier.volume18en_US
dc.identifier.issue5en_US
dc.identifier.wosWOS:000647741400013en_US
dc.identifier.scopus2-s2.0-85102190889en_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.identifier.doi10.1142/S0219887821500754-
dc.authorwosidPashaev, Oktay/T-8076-2017-
dc.identifier.wosqualityQ2-
dc.identifier.scopusqualityQ2-
item.grantfulltextopen-
item.openairetypeArticle-
item.languageiso639-1en-
item.cerifentitytypePublications-
item.fulltextWith Fulltext-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
crisitem.author.dept04.02. Department of Mathematics-
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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