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Superfluid and vortex dynamics in a fractal system were investigated by measuring the complex sheet impedance of a wire network of interconnected Sierpinski gaskets exposed to a weak magnetic field. By probing the network response over a range of length scales covering four stages of hierarchy in the gaskets, we find strong evidence for unusual scaling of the vortex energy Uₙ with the size rₕ of the loops, Uₕ{∝}rₕ^-ζ with {ζ}=ln5/3/ln2, predicted by theory.
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Meyer et al. (1991) studied this question.
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