Now showing items 1-10 of 10
New Anomalous Lieb-Robinson Bounds in Quasiperiodic XY Chains
(American Physical Society, 2014)
We announce and sketch the rigorous proof of a new kind of anomalous (or sub-ballistic) Lieb-Robinson (LR) bound for an isotropic XY chain in a quasiperiodic transversal magnetic field. Instead of the usual effective light ...
On the existence and uniqueness of global solutions for the KdV equation with quasi-periodic initial data
(American Mathematical Society, 2015)
We consider the KdV equation ∂tu+∂3xu+u∂xu=0 with quasi-periodic initial data whose Fourier coefficients decay exponentially and prove existence and uniqueness, in the class of functions which have an expansion with ...
Open Problems and Conjectures Related to the Theory of Mathematical Quasicrystals
This list of problems arose as a collaborative effort among the participants of the Arbeitsgemeinschaft on Mathematical Quasicrystals, which was held at the Mathematisches Forschungsinstitut Oberwolfach in October 2015. ...
Opening gaps in the spectrum of strictly ergodic Schrodinger operators
(European Mathematical Society, 2012)
We consider Schrodinger operators with dynamically defined potentials arising from continuous sampling along orbits of strictly ergodic transformations. The Gap Labeling Theorem states that the possible gaps in the spectrum ...
The Density of States Measure of the Weakly Coupled Fibonacci Hamiltonian
We consider the density of states measure of the Fibonacci Hamiltonian and show that, for small values of the coupling constant V , this measure is exact-dimensional and the almost everywhere value dV of the local ...
Positive Lyapunov exponents and a Large Deviation Theorem for continuum Anderson models, briefly
In this short note, we prove positivity of the Lyapunov exponent for 1D continuum Anderson models by leveraging some classical tools from inverse spectral theory. The argument is much simpler than the existing proof due ...
Multidimensional Almost-Periodic Schrödinger Operators with Cantor Spectrum
We construct multidimensional almost-periodic Schrödinger operators whose spectrum has zero lower box-counting dimension. In particular, the spectrum in these cases is a generalized Cantor set of zero Lebesgue measure.
Anderson localization for radial tree graphs with random branching numbers
We prove Anderson localization for the discrete Laplace operator on radial tree graphs with random branching numbers. Our method relies on the representation of the Laplace operator as the direct sum of half-lineﾠJacobi ...
Limit-periodic Schrödinger operators with Lipschitz continuous IDS
(American Mathematical Society, 2019)
We show that there exist limit-periodic Schrödinger operators such that the associated integrated density of states is Lipschitz continuous. These operators arise in the inverse spectral theoretic KAM approach of Pöschel.
Anderson localization for quasi-periodic CMV matrices and quantum walks
We consider CMV matrices, both standard and extended, with analytic quasi-periodic Verblunsky coefficients and prove Anderson localization in the regime of positive Lyapunov exponents. This establishes the CMV analog of a ...