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

Abstract

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 ${\tau }^{typ}\propto L^{D_1}$ and ${\Gamma }^{typ}\propto L^{-(2-D_2)}$, where $D_1$ is the information dimension and $D_2$ is the correlation dimension of eigenfunctions of the corresponding closed system.

6 pages, 8 figures

References in corpus (1)

• Exact relations between multifractal exponents at the Anderson transition

Cited by in corpus (7)

• Anderson Transitions
• Boundary multifractality in critical 1D systems with long-range hopping
• Anderson localization transition with long-ranged hoppings : analysis of the strong multifractality regime in terms of weighted Levy sums
• Statistics of the two-point transmission at Anderson localization transitions
• A critical Dyson hierarchical model for the Anderson localization transition
• Anderson transitions : multifractal or non-multifractal statistics of the transmission as a function of the scattering geometry
• Scaling properties of delay times in one-dimensional random media