The Aubry-André-Harper model provides a paradigmatic example of aperiodic order in a
one-dimensional lattice displaying a delocalization-localization phase transition at a finite …

We summarize the properties of eigenvalues and eigenfunctions of the Laplace operator in
bounded Euclidean domains with Dirichlet, Neumann, or Robin boundary condition. We …

Anderson's groundbreaking discovery that the presence of stochastic imperfections in a
crystal may result in a sudden breakdown of conductivity revolutionized our understanding …

We develop a mathematical framework allowing to study anomalous transport in
homogeneous solids. The main tools characterizing the anomalous transport properties are …

This book provides an introduction to the mathematical theory of disorder effects on quantum
spectra and dynamics. Topics covered range from the basic theory of spectra and dynamics …

Disorder is one of the predominant topics in science today. The present text is devoted to the
mathematical studyofsome particular cases ofdisordered systems. It deals with waves in …

Quantum Dynamics and Decompositions of Singular Continuous Spectra Page 1 July 5, 1995
Quantum Dynamics and Decompositions of Singular Continuous Spectra Y. Last Division of …

We review several aspects of Many‐Body Localization‐like properties exhibited by the
disordered XY chains: localization properties of the energy eigenstates and thermal states …

We introduce an enhanced multiscale analysis that yields subexponentially decaying
probabilities for bad events. For quantum and classical waves in random media, we obtain …

The multifractal dimensions D 2 μ and D 2 ψ of the energy spectrum and eigenfunctions,
respectively, are shown to determine the asymptotic scaling of the width of a spreading wave …