Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/5881
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dc.contributor.authorPashaev, Oktay-
dc.date.accessioned2017-07-07T07:29:13Z-
dc.date.available2017-07-07T07:29:13Z-
dc.date.issued2015-07-01-
dc.identifier.citationPashaev, O. (2015). Variations on a theme of q-oscillator. Physica Scripta, 90(7), 1-16. doi:10.1088/0031-8949/90/7/074010en_US
dc.identifier.issn0031-8949-
dc.identifier.urihttps://doi.org/10.1088/0031-8949/90/7/074010-
dc.identifier.urihttp://hdl.handle.net/11147/5881-
dc.description.abstractWe present several ideas in the direction of physical interpretation of q- and f-oscillators as nonlinear oscillators. First we show that an arbitrary one-dimensional integrable system in action-angle variables can be naturally represented as a classical and quantum f-oscillator. As an example, the semi-relativistic oscillator as a descriptive of the Landau levels for relativistic electron in magnetic field is solved as an f-oscillator. By using dispersion relation for q-oscillator we solve the linear q-Schrödinger equation and corresponding nonlinear complex q-Burgers equation. The same dispersion allows us to construct integrable q-NLS model as a deformation of cubic NLS in terms of recursion operator of NLS hierarchy. A peculiar property of the model is to be completely integrable at any order of expansion in deformation parameter around q = 1. As another variation on the theme, we consider hydrodynamic flow in bounded domain. For the flow bounded by two concentric circles we formulate the two circle theorem and construct the solution as the q-periodic flow by non-symmetric q-calculus. Then we generalize this theorem to the flow in the wedge domain bounded by two arcs. This two circular-wedge theorem determines images of the flow by extension of q-calculus to two bases: the real one, corresponding to circular arcs and the complex one, with q as a primitive root of unity. As an application, the vortex motion in annular domain as a nonlinear oscillator in the form of classical and quantum f-oscillator is studied. Extending idea of q-oscillator to two bases with the golden ratio, we describe Fibonacci numbers as a special type of q-numbers with matrix Binet formula. We derive the corresponding golden quantum oscillator, nonlinear coherent states and Fock-Bargman representation. Its spectrum satisfies the triple relations, while the energy levels' relative difference approaches asymptotically to the golden ratio and has no classical limit.en_US
dc.description.sponsorshipTUBITAK (110T679); Izmir Institute of Technologyen_US
dc.language.isoenen_US
dc.publisherIOP Publishing Ltd.en_US
dc.relationinfo:eu-repo/grantAgreement/TUBITAK/TBAG/110T679en_US
dc.relation.ispartofPhysica Scriptaen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectNLS hierarchyen_US
dc.subjectCircle theoremen_US
dc.subjectFibonacci numbersen_US
dc.subjectNonlinear oscillatoren_US
dc.subjectNonlinear equationsen_US
dc.titleVariations on a theme of q-oscillatoren_US
dc.typeArticleen_US
dc.authoridTR57865en_US
dc.institutionauthorPashaev, Oktay-
dc.departmentİzmir Institute of Technology. Mathematicsen_US
dc.identifier.volume90en_US
dc.identifier.issue7en_US
dc.identifier.startpage1en_US
dc.identifier.endpage16en_US
dc.identifier.wosWOS:000357541800011en_US
dc.identifier.scopus2-s2.0-84936873143en_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.identifier.doi10.1088/0031-8949/90/7/074010-
dc.relation.doi10.1088/0031-8949/90/7/074010en_US
dc.coverage.doi10.1088/0031-8949/90/7/074010en_US
dc.identifier.wosqualityQ2-
dc.identifier.scopusqualityQ2-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.fulltextWith Fulltext-
item.openairetypeArticle-
item.languageiso639-1en-
item.cerifentitytypePublications-
item.grantfulltextopen-
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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