A rigorous replica trick approach to Anderson localization in one dimension

DOI10.1007/BF01463399zbMath0614.60098OpenAlexW2067586198MaRDI QIDQ1819840

J. Fernando Perez, Abel Klein, Fabio Martinelli

Publication date: 1986

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01463399

zbMATH Keywords

Dirichlet boundary conditionsexponential localizationreplica trickfield theoretic methods

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) (60J70) Stochastic mechanics (including stochastic electrodynamics) (81P20)

Related Items

Supersymmetric cluster expansions and applications to random Schrödinger operators ⋮ The density of states in the Anderson model at weak disorder: A renormalization group analysis of the hierarchical model ⋮ Smoothness of the density of states in the Anderson model at high disorder ⋮ Spreading of wave packets in the Anderson model on the Bethe lattice ⋮ Frequency concentration and location lengths for the Anderson model at small disorders ⋮ Quantitative Anderson localization of Schrödinger eigenstates under disorder potentials ⋮ The supersymmetric transfer matrix for linear chains with nondiagonal disorder. ⋮ The density of states of 1D random band matrices via a supersymmetric transfer operator ⋮ Supersymmetric polar coordinates with applications to the Lloyd model ⋮ Anderson localization for Bernoulli and other singular potentials ⋮ Spectral theory of random self-adjoint operators ⋮ Localization for one-dimensional, continuum, Bernoulli-Anderson models.

Cites Work

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• Continuous singular measures with small Fourier-Stieltjes transforms
• Anderson localization for Bernoulli and other singular potentials