Resonance width distribution for high-dimensional random media

Abstract

We study the distribution of resonance widths P(Γ) for three-dimensional (3D) random scattering media and analyze how it changes as a function of the randomness strength. We are able to identify in P(Γ) the system-inherent fingerprints of the metallic, localized, and critical regimes. Based on the properties of resonance widths, we also suggest a new criterion for determining and analyzing the metal-insulator transition. Our theoretical predictions are verified numerically for the prototypical 3D tight-binding Anderson model.

Finite-size scaling analysis of localization transition for scalar waves in a three-dimensional ensemble of resonant point scatterers

“…Obviously, g n is a random quantity and only its statistical properties are meaningful. Statistical distributions of decay rates Γ/2 and normalized decay rates g defined in a way analogous to ours have been previously studied for the tight-binding Hamiltonian of the open 3D Anderson model [25,26]. It was shown that these distributions bear clear signatures of localization transition and that p(g) takes a universal shape at the critical point, but a quantitative analysis allowing for estimating the critical exponents of the transition was not peformed.…”

Statistics of resonances in one-dimensional disordered systems

“…This asymptotic (1/Γ)-behavior is universal, in the sense that it holds for any degree of disorder and for any −2t < E < 2t. The 1/Γ-asymptotics can be understood with the help of a simple intuitive argument which, in somewhat different versions, has appeared in [9][10][11][12]25]. The essence of the argument is that narrow resonances stem from states localized far away from the open boundary, say, at distance x.…”

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

“…17 They determine the conductance fluctuations of a quantum dot in the Coulomb blockade regime 32 or the current relaxation. 3 The poles of the scattering matrix show up as resonances, which are the complex eigenvalues E n = E n − iΓ n /2 of H eff .…”

“…7 Recently, several works have been devoted to deepen our understanding of the scattering properties of disordered systems by analyzing the distribution of resonance widths and Wigner delay times. 8,9,10,11,12,13,14,16,17 Both distribution functions have been shown to be closely related to the properties of the corresponding closed system, i.e., the fractality of the eigenstates and the critical features of the MIT. In this respect, detailed analysis have been performed for the three-dimensional (3D) Anderson model 14 and also for the power law band random matrix (PBRM) model.…”