We investigate the Anderson metal-insulator transition for random Schrödinger operators.
We define the strong insulator region to be the part of the spectrum where the random …

We investigate a group B• that includes Artin's braid group B∞ and Thompson's group F.
The elements of B• are represented by braids diagrams in which the distances between the …

We study the spectrum of the Fibonacci Hamiltonian and prove upper and lower bounds for
its fractal dimension in the large coupling regime. These bounds show that as λ → ∞,\rm dim …

Transfer matrices and transport for Schrödinger operators Page 1 ANNA L E S D E L’INSTITU
T FO U RIER ANNALES DE L’INSTITUT FOURIER François GERMINET, Alexander …

We derive a general upper bound on the spreading rate of wavepackets in the framework of
Schrödinger time evolution. Our result consists of showing that a portion of the wavepacket …

We develop a general method to bound the spreading of an entire wavepacket under
Schrödinger dynamics from above. This method derives upper bounds on time-averaged …

We present an approach to quantum dynamical lower bounds for discrete one-dimensional
Schrödinger operators which is based on power-law bounds on transfer matrices. It suffices …

We develop tools to study arithmetically induced singular continuous spectrum in the
neighborhood of the arithmetic transition in the hyperbolic regime. This leads to first …

We introduce a notion of ˇ-almost periodicity and prove quantitative lower spectral/quantum
dynamical bounds for general bounded ˇ-almost periodic potentials. Applications include the …

We consider ergodic families of Schrödinger operators over base dynamics given by strictly
ergodic subshifts on finite alphabets. It is expected that the majority of these operators have …