Scattering at the Anderson transition: Power--law banded random matrix model

Details Scattering at the Anderson transition: Power--law banded random matrix model Scattering at the Anderson transition: Power--law banded random matrix model

2006-02-10

arxiv.org/abs/cond-mat/0602265v2

Phys. Rev. B 74, 125114 (2006).

Physics

Condensed Matter

Disordered Systems and Neural Networks

6 pages, 8 figures

Scientific paper

10.1103/PhysRevB.74.125114

We analyze the scattering properties of a periodic one-dimensional system at criticality represented by the so-called power-law banded random matrix model at the metal insulator transition. We focus on the scaling of Wigner delay times $\tau$ and resonance widths $\Gamma$. We found that the typical values of $\tau$ and $\Gamma$ (calculated as the geometric mean) scale with the system size $L$ as $\tau^{\tiny typ}\propto L^{D_1}$ and $\Gamma^{\tiny typ} \propto L^{-(2-D_2)}$, where $D_1$ is the information dimension and $D_2$ is the correlation dimension of eigenfunctions of the corresponding closed system.

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