One-dimensional Anderson Localization: distribution of wavefunction amplitude and phase at the band center
Year: 2009
Type: conference-paper
Abstract: The statistics of normalized wavefunctions in the one‐dimensional (1d) Anderson model of localization is considered. It is shown that at any energy that corresponds to a rational filling factor f = pq there is a statistical anomaly which is seen in expansion of the generating function (GF) to the order q−2 in the disorder parameter. We study in detail the principle anomaly at f = 12 that appears in the leading order. The transfer‐matrix equation of the Fokker‐Planck type with a two‐dimensional internal space is derived for GF. It is shown that the zero‐mode variant of this equation is integrable and a solution for the generating function is found in the thermodynamic limit.
Source: AIP conference proceedings
DOI: 10.1063/1.3149496
Authors: V. E. Kravtsov, V. I. Yudson, Vladimir Lebedev, Mikhail Feigel’man
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1592118045