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Title: Vortex images, q-calculus and entangled coherent states
Authors: Pashaev, Oktay
Keywords: Quantum entanglement
Vortex flow
Dimensionless parameters
Jackson q-integral
Publisher: IOP Publishing Ltd.
Source: Pashaev, O. (2012). Vortex images, q-calculus and entangled coherent states. Journal of Physics: Conference Series, 343. doi:10.1088/1742-6596/343/1/012093
Abstract: The two circles theorem for hydrodynamic flow in annular domain bounded by two concentric circles is derived. Complex potential and velocity of the flow are represented as q-periodic functions and rewritten in terms of the Jackson q-integral. This theorem generalizes the Milne-Thomson one circle theorem and reduces to the last on in the limit q → ∞. By this theorem problem of vortex images in annular domain between coaxial cylinders is solved in terms of q-elementary functions. An infinite set of images, as symmetric points under two circles, is determined completely by poles of the q-logarithmic function, where dimensionless parameter q = r 2 2/r 1 2 is given by square ratio of the cylinder radii. Motivated by Möbius transformation for symmetrical points under generalized circle in complex plain, the system of symmetric spin coherent states corresponding to antipodal qubit states is introduced. By these states we construct the maximally entangled orthonormal two qubit spin coherent state basis, in the limiting case reducible to the Bell basis. Average energy of XYZ model in these states, describing finite localized structure with characteristic extremum points, appears as an energy surface in maximally entangled two qubit space. Generalizations to three and higher multiple qubits are found. We show that our entangled N qubit states are determined by set of complex Fibonacci and Lucas polynomials and corresponding Binet-Fibonacci q-calculus.
Description: 7th International Conference on Quantum Theory and Symmetries, QTS7; Prague; Czech Republic; 7 August 2011 through 13 August 2011
ISSN: 1742-6588
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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