One-dimensional Anderson Localization: distribution of wavefunction amplitude and phase at the band center

Journal Article · Thu May 14 00:00:00 EDT 2009 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.3149496· OSTI ID:21304871

Kravtsov, V E ^[1]; Yudson, V I ^[2]

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1. Abdus Salam International Centre for Theoretical Physics, P.O.B. 586, 34100 Trieste (Italy)
2. Landau Institute for Theoretical Physics, 2 Kosygina St., 117940 Moscow (Russian Federation)

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 = (p/q) 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 = (1/2) 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.

• OSTI ID: 21304871
• Journal Information: AIP Conference Proceedings, Vol. 1134, Issue 1; Conference: Landau memorial conference on advances in theoretical physics, Chernogolovka (Russian Federation), 22-26 Jun 2008; Other Information: DOI: 10.1063/1.3149496; (c) 2009 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
BAND THEORY
CHIRAL SYMMETRY
FOKKER-PLANCK EQUATION
HAMILTONIANS
HARMONIC OSCILLATORS
HUBBARD MODEL
MATHEMATICAL SOLUTIONS
MATRICES
ONE-DIMENSIONAL CALCULATIONS
THERMODYNAMICS
TRANSFER FUNCTIONS
TWO-DIMENSIONAL CALCULATIONS
WAVE FUNCTIONS