Exact solution for eigenfunction statistics at the center-of-band anomaly in the Anderson localization model

Abstract

An exact solution is found for the problem of the center-of-band ($E=0$) anomaly in the one-dimensional (1D) Anderson model of localization. By deriving and solving an equation for the generating function $\Phi (u,\varphi )$ we obtained an exact expression in quadratures for statistical moments $I_q=⟨|{\psi }_E(\mathbf{r}){|}^{2q}⟩$ of normalized wavefunctions ${\psi }_E(\mathbf{r})$ which show violation of one-parameter scaling and emergence of an additional length scale at $E\approx 0$.

5 pages, 2 figures

References in corpus (4)

• Anderson Transitions
• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Band-center anomaly of the conductance distribution in one-dimensional Anderson localization
• Scaling and the center of band anomaly in a one-dimensional Anderson model with diagonal disorder

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• Absolutely continuous energy bands in the electronic spectrum of quasiperiodic ladder networks
• Decoherence-induced conductivity in the discrete 1D Anderson model: A novel approach to even-order generalized Lyapunov exponents
• Anomalous localization enhancement in one-dimensional non-Hermitian disordered lattices
• Statistics of anomalously localized states at the center of band E=0 in the one-dimensional Anderson localization model