Strategies in localization proofs for one-dimensional random Schrödinger operators. (English) Zbl 1002.60062

Stolz, Günter

Proc. Indian Acad. Sci., Math. Sci. 112, No. 1, 229-243 (2002).

Author’s abstract: Recent results on localization, both exponential and dynamical, for various models of one-dimensional, continuum, random Schrödinger operators are reviewed. This includes Anderson models with indefinite single site potentials, the Bernoulli-Anderson model, the Poisson model, and the random displacement model. Among the tools which are used to analyse these models are generalized spectral averaging techniques and results from inverse spectral and scattering theory. A discussion of open problems is included.

Reviewer: Andrzej Nowak (Katowice)

MSC:

60H25	Random operators and equations (aspects of stochastic analysis)
47B80	Random linear operators
82B44	Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics

Keywords:

localization; Schrödinger operator; random potential

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