Abstract
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.
Highlights
Method of Images The problem of vortex images in circular annulus was formulated by Poincare [1] and solved by q-elementary functions in [2]
In the present paper we are generalizing these results by studying arbitrary hydrodynamic flow in annular domain bounded by two concentric circles
We describe the method of images implications for quantum qubit states
Summary
Method of Images The problem of vortex images in circular annulus was formulated by Poincare [1] and solved by q-elementary functions in [2]. It was shown that all images are ordered in geometric progression and are determined by singularities of q-logarithmmic and q-exponential functions. By this approach we solved one and two vortex problems in circular annulus [3] and found regular polygon type N vortex configurations [2]. In the present paper we are generalizing these results by studying arbitrary hydrodynamic flow in annular domain bounded by two concentric circles. We formulate general two circle theorem and find self-similar structure of the flow. We describe the method of images implications for quantum qubit states
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