Anomalous localisation near the band centre in the 1D Anderson model: Hamiltonian map approach

2011/12/12 by L. Tessieri, I. F. Herrera-González, F. M. Izrailev · 16 citations
Mathematics · Physics and Astronomy · #Anderson impurity model #Diagonal #Geometry #Hamiltonian (control theory) #Mathematical optimization #Mathematical physics #Mathematics #Physics #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Quantum mechanics #Scaling #Scaling law #Semiconductor Quantum Structures and Devices #Statistical physics #cond-mat.dis-nn

paper · pdf · doi:10.1016/j.physe.2012.01.024

published in Physica E Low-dimensional Systems and Nanostructures 44(7-8), 1260-1266 (Elsevier BV) · 23 pages, 4 figures

arxiv created 2011/12/12 · openalex publication_date 2012/02/03 · arxiv updated 2012/06/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We present a full analytical solution for the localisation length in the one-dimensional Anderson model with weak diagonal disorder in the vicinity of the band centre. The results are obtained with the Hamiltonian map approach that turns out to be more effective than other known methods. The analytical expressions are supported by numerical data. We also discuss the implications of our results for the single-parameter scaling hypothesis.

Citations

• One-dimensional quantum models with correlated disorder versus classical oscillators with colored noise
• Scaling and the Center-of-Band Anomaly in a One-Dimensional Anderson Model with Diagonal Disorder
• Scaling Theory of Localization: Absence of Quantum Diffusion in Two Dimensions