Large-coupling-constant behavior of the Liapunov exponent in a binary alloy
Journal Article
·
· J. Stat. Phys.; (United States)
The authors consider the usual one-dimensional tight-binding Anderson model with the random potential taking only two values, 0 and lambda, with probability p and 1-p, 0 < p < 1. The authors show that the Liapunov exponent ..gamma../sub lambda/ (E), E epsilon R, diverges as lambda ..-->.. infinity uniformly in the energy E. Using a result of Carmona, Klein, and Martinelli, this proves that for lambda large enough, the integrated density of states is singular continuous. They also compute explicitly the exact asymptotics for a dense set of energies and they compare the results with numerical simulations.
- Research Organization:
- Universita di Roma La Sapienza (Italy)
- OSTI ID:
- 5264449
- Journal Information:
- J. Stat. Phys.; (United States), Journal Name: J. Stat. Phys.; (United States) Vol. 48:1/2; ISSN JSTPB
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALLOY SYSTEMS
BINARY ALLOY SYSTEMS
BOUNDARY CONDITIONS
COUPLING CONSTANTS
CRYSTAL MODELS
DIFFERENTIAL EQUATIONS
ENERGY-LEVEL DENSITY
EQUATIONS
ERGODIC HYPOTHESIS
HYPOTHESIS
LYAPUNOV METHOD
MATHEMATICAL MODELS
MECHANICS
MONTE CARLO METHOD
ONE-DIMENSIONAL CALCULATIONS
PARTIAL DIFFERENTIAL EQUATIONS
PROBABILITY
QUANTUM MECHANICS
RANDOMNESS
SCHROEDINGER EQUATION
STATISTICAL MECHANICS
WAVE EQUATIONS
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALLOY SYSTEMS
BINARY ALLOY SYSTEMS
BOUNDARY CONDITIONS
COUPLING CONSTANTS
CRYSTAL MODELS
DIFFERENTIAL EQUATIONS
ENERGY-LEVEL DENSITY
EQUATIONS
ERGODIC HYPOTHESIS
HYPOTHESIS
LYAPUNOV METHOD
MATHEMATICAL MODELS
MECHANICS
MONTE CARLO METHOD
ONE-DIMENSIONAL CALCULATIONS
PARTIAL DIFFERENTIAL EQUATIONS
PROBABILITY
QUANTUM MECHANICS
RANDOMNESS
SCHROEDINGER EQUATION
STATISTICAL MECHANICS
WAVE EQUATIONS