Anderson localization for one-dimensional difference Schroedinger operator with quasiperiodic potential

Journal Article · Sun Mar 01 04:00:00 EST 1987 · J. Stat. Phys.; (United States)

DOI:https://doi.org/10.1007/BF01011146· OSTI ID:6459511

Sinai, Ya G

The Schroedinger difference operator considered here has the form (H/sub epsilon/(..cap alpha..)psi)(n) = -epsilon(psi(n + 1) + psi(n - 1)) + V(nomega + ..cap alpha..psi(n) where V is a C/sup 2/-periodic Morse function taking each value at not more than two points. It is shown that for sufficiently small epsilon the operator H/sub epsilon/(..cap alpha..) has for a.e. ..cap alpha.. a pure point spectrum. The corresponding eigenfunctions decay exponentially outside a finite set. The integrated density of states is an incomplete devil's staircase with infinitely many flat pieces.

• Research Organization: L. D. Landau Institute of Theoretical Physics, Moscow, USSR
• OSTI ID: 6459511
• Journal Information: J. Stat. Phys.; (United States), Journal Name: J. Stat. Phys.; (United States) Vol. 46:5/6; ISSN JSTPB
• Country of Publication: United States
• Language: English

Related Subjects

645400 -- High Energy Physics-- Field Theory
657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CRYSTAL LATTICES
CRYSTAL MODELS
CRYSTAL STRUCTURE
DIFFERENTIAL EQUATIONS
EIGENFUNCTIONS
EIGENVALUES
EQUATIONS
FIELD THEORIES
FUNCTIONS
GREEN FUNCTION
HAMILTONIANS
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MECHANICS
MORSE POTENTIAL
ONE-DIMENSIONAL CALCULATIONS
PARTIAL DIFFERENTIAL EQUATIONS
PERTURBATION THEORY
POTENTIALS
PROBABILITY
QUANTIZATION
QUANTUM FIELD THEORY
QUANTUM MECHANICS
QUANTUM OPERATORS
RENORMALIZATION
SCHROEDINGER EQUATION
SPECTRA
STATISTICAL MECHANICS
TUNNEL EFFECT
WAVE EQUATIONS