Weak disorder expansion of the invariant measure for the one-dimensional Anderson model

Journal Article · Sun May 01 00:00:00 EDT 1988 · J. Stat. Phys.; (United States)

DOI:https://doi.org/10.1007/BF01028469· OSTI ID:6140345

Bovier, A; Klein, A

We show that the formal perturbation expansion of the invariant measure for the Anderson model in one dimension has singularities at all energies E/sub 0/ = 2 cos ..pi..(p/q); we derive a modified expansion near these energies that we show to have finite coefficients to all orders. Moreover, we show that the first q - 3 of them coincide with those of the naive expansion, while there is an anomaly in the (q - 2)th term. This also gives a weak disorder expansion for the Liapunov exponent and for the density of states. This generalizes previous results of Kappus and Wegner and of Derrida and Gardner.

• Research Organization: Univ. of California, Irvine (USA)
• OSTI ID: 6140345
• Journal Information: J. Stat. Phys.; (United States), Vol. 51:3-4
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CRYSTAL MODELS
INVARIANCE PRINCIPLES
ELECTRONS
ENERGY LEVELS
ENERGY-LEVEL DENSITY
HAMILTONIANS
LYAPUNOV METHOD
MARKOV PROCESS
ONE-DIMENSIONAL CALCULATIONS
ORDER PARAMETERS
PERTURBATION THEORY
SERIES EXPANSION
STATISTICAL MECHANICS
TRANSPORT THEORY
ELEMENTARY PARTICLES
FERMIONS
LEPTONS
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MECHANICS
QUANTUM OPERATORS
STOCHASTIC PROCESSES
656002* - Condensed Matter Physics- General Techniques in Condensed Matter- (1987-)
657002 - Theoretical & Mathematical Physics- Classical & Quantum Mechanics