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

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.

23 pages, 4 figures

References in corpus (9)

• Anomalous Localization in Low-Dimensional Systems with Correlated Disorder
• Single parameter scaling in one-dimensional localization revisited
• Classical Representation of the 1D Anderson Model
• 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
• Anderson localization as a parametric instability of the linear kicked oscillator
• 1D quantum models with correlated disorder vs. classical oscillators with coloured noise
• Crossover of conductance and local density of states in a single-channel disordered quantum wire
• Unified description of perturbation theory and band center anomaly in one-dimensional Anderson localization

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• Anomalous localization enhancement in one-dimensional non-Hermitian disordered lattices
• The band-centre anomaly in the 1D Anderson model with correlated disorder
• Two parameter scaling in the crossover from symmetry class BDI to AI
• Localization transitions in quadratic systems without quantum chaos