Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection

Permanent URI for this collectionhttps://hdl.handle.net/11147/7148

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Author: search.filters.author.Pashaev, OktayInstitution Author: search.filters.institutionAuthor.Pashaev, Oktay K.

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Now showing 1 - 3 of 3
  • Conference Object
    Citation - WoS: 2
    Citation - Scopus: 2
    Quantum Group Symmetry for Kaleidoscope of Hydrodynamic Images and Quantum States
    (IOP Publishing, 2019) Pashaev, Oktay
    The hydrodynamic flow in several bounded domains can be formulated by the image theorems, like the two circle, the wedge and the strip theorems, describing flow by q-periodic functions. Depending on geometry of the domain, parameter q has different geometrical meanings and values. In the special case of the wedge domain, with q as a primitive root of unity, the set of images appears as a regular polygon kaleidoscope. By interpreting the wave function in the Fock-Barman representation as complex potential of a flow, we find modn projection operators in the space of quantum coherent states, related with operator q-numbers. They determine the units of quantum information as kaleidoscope of quantum states with quantum group symmetry of the q-oscillator. Expansion of Glauber coherent states to these units and corresponding entropy are discussed.
  • Conference Object
    Citation - Scopus: 5
    Kaleidoscope of Classical Vortex Images and Quantum Coherent States
    (Springer, 2018) Pashaev, Oktay; Koçak, Aygül
    The Schrödinger cat states, constructed from Glauber coherent states and applied for description of qubits are generalized to the kaleidoscope of coherent states, related with regular n-polygon symmetry and the roots of unity. This quantum kaleidoscope is motivated by our method of classical hydrodynamics images in a wedge domain, described by q-calculus of analytic functions with q as a primitive root of unity. First we treat in detail the trinity states and the quartet states as descriptive for qutrit and ququat units of quantum information. Normalization formula for these states requires introduction of specific combinations of exponential functions with mod 3 and mod 4 symmetry, which are known also as generalized hyperbolic functions. We show that these states can be generated for an arbitrary n by the Quantum Fourier transform and can provide in general, qudit unit of quantum information. Relations of our states with quantum groups and quantum calculus are discussed. © Springer Nature Switzerland AG 2018.
  • Article
    Citation - WoS: 13
    Citation - Scopus: 14
    On a 2+1-Dimensional Whitham-Broer System: a Resonant Nls Connection
    (John Wiley and Sons Inc., 2011) Rogers, Colin; Pashaev, Oktay
    It is established that the Whitham-Broer-Kaup shallow water system and the "resonant" nonlinear Schrödinger equation are equivalent. A symmetric integrable 2+1-dimensional version of the Whitham-Broer-Kaup system is constructed which, in turn, is equivalent to a recently introduced resonant Davey-Stewartson I system incorporating a Madelung-Bohm type quantum potential. A bilinear representation is adopted and resonant solitonic interaction in this new 2+1-dimensional Kaup-Broer system is exhibited.