Absolutely continuous spectrum for the Anderson model on a product of a tree with a finite graph

Froese, Richard; Halasan, Florina; Hasler, David

doi:10.48550/arxiv.1008.2949

Cited by 3 publications

(3 citation statements)

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“…This is known as the extended states conjecture. However, it has only been proven in the case of regular trees [ASW,FHS2,Kl1,Kl2] and in strongly related models [FHH,FHS3,FHS4,Hal1,KlS].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Absolutely continuous spectrum for random operators on trees of finite cone type

Keller

Lenz

Warzel

2012

JAMA

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We study the spectrum of random operators on a large class of trees. These trees have finitely many cone types and they can be constructed by a substitution rule. The random operators are perturbations of Laplace type operators either by random potentials or by random hopping terms, i.e., perturbations of the off-diagonal elements. We prove stability of arbitrary large parts of the absolutely continuous spectrum for sufficiently small but extensive disorder.

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“…This is known as the extended states conjecture. However, it has only been proven in the case of regular trees [ASW,FHS2,Kl1,Kl2] and in strongly related models [FHH,FHS3,FHS4,Hal1,KlS].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Absolutely continuous spectrum for random operators on trees of finite cone type

Keller

Lenz

Warzel

2012

JAMA

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“…After the seminal work of Klein [Kl1,Kl2] there has been a lot of effort in the recent years to develop various techniques to show preservation of absolutely continuous spectrum for random operators on tree like graphs, see [ASW,AW,FHH,FHS2,FHS3,Hal,Ke,KLW2,KS1,KS2]. While most of the work is concerned with diagonal perturbations by a random potential, we consider a randomization of the geometry.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Absolutely Continuous Spectrum for Multi-type Galton Watson Trees

Keller

2012

Ann. Henri Poincaré

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“…Different techniques to obtain absolutely continuous spectrum for the Anderson model on the Bethe lattice and similar tree like structures have been developed in [AiSW,FHS1,FHH,H,KLW,FHS2,AiW]. The hyperbolic geometry methods of [FHS1,H] were extended to the Anderson model on a Bethe strip of connectivity K = 2 and width m = 2 in [FHH].…”

Section: Introductionmentioning

confidence: 99%

Ballistic behavior for random Schrödinger operators on the Bethe strip

Klein¹,

Sadel²

2011

J. Spectr. Theory

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Abstract. The Bethe strip of width m is the Cartesian product B f1; : : : ; mg, where B is the Bethe lattice (Cayley tree). We consider Anderson-like Hamiltonians H D 1 2 ˝1 C 1˝A C V on a Bethe strip with connectivity K 2, where A is an m m symmetric matrix, V is a random matrix potential, and is the disorder parameter. Under certain conditions on A and K, for which we previously proved the existence of absolutely continuous spectrum for small , we now obtain ballistic behavior for the spreading of wave packets evolving under H for small . Mathematics Subject Classification (2010). Primary 82B44; Secondary 47B80, 60H25.

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Absolutely continuous spectrum for the Anderson model on a product of a tree with a finite graph

Cited by 3 publications

References 0 publications

Absolutely continuous spectrum for random operators on trees of finite cone type

Absolutely continuous spectrum for random operators on trees of finite cone type

Absolutely Continuous Spectrum for Multi-type Galton Watson Trees

Ballistic behavior for random Schrödinger operators on the Bethe strip

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