Absolutely continuous spectrum implies ballistic transport for quantum particles in a random potential on tree graphs

Abstract

We discuss the dynamical implications of the recent proof that for a quantum particle in a random potential on a regular tree graph absolutely continuous spectrum occurs non-perturbatively through rare fluctuation-enabled resonances. The main result is spelled in the title.

Corrected version

References in corpus (6)

• Resonant delocalization for random Schrödinger operators on tree graphs
• Anomalous heat-kernel decay for random walk among bounded random conductances
• Extended States in a Lifshitz Tail Regime for Random Schrödinger Operators on Trees
• Absence of mobility edge for the Anderson random potential on tree graphs at weak disorder
• Much Ado About Something: Why Lieb-Robinson bounds are useful
• Ballistic Behavior for Random Schrödinger Operators on the Bethe Strip

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• Critical behavior of the Anderson model on the Bethe lattice via a large-deviation approach
• Anderson Localization on the Bethe Lattice using Cages and the Wegner Flow
• The Large Connectivity Limit of the Anderson Model on Tree Graphs
• Fully localized and partially delocalized states in the tails of Erdös-Rényi graphs in the critical regime
• Lieb-Robinson bounds and strongly continuous dynamics for a class of many-body fermion systems in ${\mathbb{R}}^d$
• Ballistic Transport in One-Dimensional Quasi-Periodic Continuous Schrödinger Equation
• Ballistic Motion in One-Dimensional Quasi-Periodic Discrete Schrödinger Equation
• Quantum ergodicity for the Anderson model on regular graphs
• Anderson transition at 2 dimensional growth rate on antitrees and spectral theory for operators with one propagating channel
• Surprises in the phase diagram of the Anderson model on the Bethe lattice
• Absolutely Continuous Spectrum for random Schroedinger operators on the Fibonacci and similar tree-strips
• Absolutely Continuous Spectrum for Quantum Trees
• Progress in the mathematical theory of quantum disordered systems
• Ballistic Transport and Absolute Continuity of One-Frequency Schrödinger Operators