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Relation between the Correlation Dimensions of Multifractal Wavefunctions and Spectral Measures in Integer Quantum Hall Systems

B. Huckestein·L. Schweitzer
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Abstract

We study the time evolution of wavepackets of non-interacting electrons in a two-dimensional disordered system in strong magnetic field. For wavepackets built from states near the metal-insulator transition in the center of the lowest Landau band we find that the return probability to the origin $p(t)$ decays algebraically, $p(t) \sim t^{-D_2/2}$, with a non-conventional exponent $D_2/2$. $D_2$ is the generalized dimension describing the scaling of the second moment of the wavefunction. We show that the corresponding spectral measure is multifractal and that the exponent $D_2/2$ equals the generalized dimension $\widetilde{D}_2$ of the spectral measure.

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B. Huckestein, L. Schweitzer. 1994-01-26. Relation between the Correlation Dimensions of Multifractal Wavefunctions and Spectral Measures in Integer Quantum Hall Systems. https://doi.org/10.1103/physrevlett.72.713

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