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Probing the eigenfunction fractality with a stop watch

J. A. Mendez-Bermudez·Tsampikos Kottos
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Abstract

We study numerically the distribution of scattering phases ${\cal P}(Φ)$ and of Wigner delay times ${\cal P}(τ_W)$ for the power-law banded random matrix (PBRM) model at criticality with one channel attached to it. We find that ${\cal P}(Φ)$ is insensitive to the position of the channel and undergoes a transition towards uniformity as the bandwidth $b$ of the PBRM model increases. The inverse moments of Wigner delay times scale as $<τ_W^{-q} >\sim L^{- q D_{q+1}}$, where $D_q$ are the multifractal dimensions of the eigenfunctions of the corresponding closed system and $L$ is the system size. The latter scaling law is sensitive to the position of the channel.

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J. A. Mendez-Bermudez, Tsampikos Kottos. 2005-03-30. Probing the eigenfunction fractality with a stop watch. https://doi.org/10.1103/physrevb.72.064108

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