Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7148
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Conference Object Method of Hydrodynamic Images and Quantum Calculus in Fock-Bargmann Representation of Quantum States(Springer, 2024) Pashaev, Oktay; 01. Izmir Institute of Technology; 04.02. Department of Mathematics; 04. Faculty of ScienceWe propose a new approach to quantum states in Fock space in terms of classical hydrodynamics. By conformal mapping of complex analytic function, representing the wave function of quantum states in Fock-Bargmann representation, we define the complex potential, describing these quantum states by incompressible and irrotational classical hydrodynamic flow. In our approach, zeros of the wave function appear as a set of point vortices (sources) in plane with the same strength, allowing interpretation of them as images in a bounded domain. For the cat states we find fluid representation as descriptive of a point source in the oblique strip domain, with infinite number of periodically distributed images. For the annular domain, the infinite set of images is described by Jackson q-exponential functions. We show that these functions represent the wave functions of quantum coherent states of the q-deformed quantum oscillator in q-Fock-Bargmann representation and describe the infinite set of point vortices, distributed in geometric progression. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.Conference Object Citation - Scopus: 5Kaleidoscope of Classical Vortex Images and Quantum Coherent States(Springer, 2018) Pashaev, Oktay; Pashaev, Oktay; Koçak, Aygül; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of TechnologyThe 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.