Spectral properties of dynamical localization for Schr\"odinger operators
Fran\c{c}ois Germinet, Amal Taarabt
TL;DR
This paper explores the relationship between dynamical localization and eigenfunction localization in Schrödinger operators, establishing equivalences and providing counterexamples to demonstrate optimality.
Contribution
It introduces three classes of equivalent localization properties and analyzes their interrelations, advancing understanding of spectral localization in quantum systems.
Findings
Identifies three classes of equivalent localization properties.
Shows the relationships between these classes are optimal.
Provides counterexamples to demonstrate the limits of these equivalences.
Abstract
We investigate the equivalence between dynamical localization and localization properties of eigenfunctions of Schr\"odinger Hamiltonians. We introduce three classes of equivalent properties and study the relationships between them. These relationships are shown to be optimal thanks to counter examples.
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