Two-circles theorem, q-periodic functions and entangled qubit states

Physics and Mathematics of Nonlinear Phenomena 2013

Pashaev, Oktay K.^1

Department of Mathematics, Izmir Institute of Technology, Gulbahce Campus, Izmir, Urla 35430, Turkey^1

关键词: Analytic functions;    Complex potentials;    Elementary function;    Geometric patterns;    Hydrodynamic flows;    Periodic modulation;    Q-difference equation;    Self-similar fractals;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/482/1/012033/pdf
DOI  :  10.1088/1742-6596/482/1/012033

来源: IOP

【 摘 要 】

For arbitrary hydrodynamic flow in circular annulus we introduce the two circle theorem, allowing us to construct the flow from a given one in infinite plane. Our construction is based on q-periodic analytic functions for complex potential, leading to fixed scale-invariant complex velocity, where q is determined by geometry of the region. Self-similar fractal structure of the flow with q-periodic modulation as solution of q-difference equation is studied. For one point vortex problem in circular annulus by fixing singular points we find solution in terms of q-elementary functions. Considering image points in complex plane as a phase space for qubit coherent states we construct Fibonacci and Lucas type entangled N-qubit states. Complex Fibonacci curve related to this construction shows reach set of geometric patterns.