Now showing items 1-5 of 5
On the existence and uniqueness of global solutions for the KdV equation with quasi-periodic initial data
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. ...
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 ...
Opening gaps in the spectrum of strictly ergodic Schrodinger operators
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 ...
New Anomalous Lieb-Robinson Bounds in Quasiperiodic XY Chains
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 ...