Absolutely Continuous Spectrum for random Schroedinger operators on the Fibonacci and similar tree-strips

Abstract

We will consider cross products of finite graphs with a class of trees that have arbitrarily but finitely long line segments, such as the Fibonacci tree. Such cross products are called tree-strips. We prove that for small disorder random Schrödinger operators on such tree-strips have purely absolutely continuous spectrum in a certain set.

30 pages, two figures; result improved, contains a certain class of tree-strips

References in corpus (5)

• Absolutely continuous spectrum implies ballistic transport for quantum particles in a random potential on tree graphs
• Localization for the Anderson Model on Trees with Finite Dimensions
• Ballistic Behavior for Random Schrödinger Operators on the Bethe Strip
• Absolutely Continuous Spectrum for Random Schroedinger Operators on Tree-Strips of finite cone type
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Cited by in corpus (4)

• Anderson transition at 2 dimensional growth rate on antitrees and spectral theory for operators with one propagating channel
• Spectral Theory of one-channel operators and application to absolutely continuous spectrum for Anderson type models
• A central limit theorem for products of random matrices and GOE statistics for the Anderson model on long boxes
• On absolutely continuous spectrum for one-channel unitary operators