Browsing Mathematics Department by Author "Damanik, David"
Now showing items 19 of 9

Anderson localization for quasiperiodic CMV matrices and quantum walks
Wang, Fengpeng; Damanik, David (2019)We consider CMV matrices, both standard and extended, with analytic quasiperiodic Verblunsky coefficients and prove Anderson localization in the regime of positive Lyapunov exponents. This establishes the CMV analog of a ... 
Anderson localization for radial tree graphs with random branching numbers
Damanik, David; Sukhtaiev, Selim (2019)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 halflineﾠJacobi ... 
The Density of States Measure of the Weakly Coupled Fibonacci Hamiltonian
Damanik, David; Gorodetski, Anton (2012)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 exactdimensional and the almost everywhere value dV of the local ... 
Limitperiodic Schrödinger operators with Lipschitz continuous IDS
Damanik, David; Fillman, Jake (2019)We show that there exist limitperiodic 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. 
Multidimensional AlmostPeriodic Schrödinger Operators with Cantor Spectrum
Damanik, David; Fillman, Jake; Gorodetski, Anton (2019)We construct multidimensional almostperiodic Schrödinger operators whose spectrum has zero lower boxcounting dimension. In particular, the spectrum in these cases is a generalized Cantor set of zero Lebesgue measure. 
New Anomalous LiebRobinson Bounds in Quasiperiodic XY Chains
Damanik, David; Lemm, Marius; Lukic, Milivoje; Yessen, William (2014)We announce and sketch the rigorous proof of a new kind of anomalous (or subballistic) LiebRobinson (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 quasiperiodic initial data
Damanik, David; Goldstein, Michael (2015)We consider the KdV equation ∂tu+∂3xu+u∂xu=0 with quasiperiodic 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
Adiceam, Faustin; Damanik, David; Gähler, Franz; Grimm, Uwe; Haynes, Alan; Julien, Antoine; Navas, Andrés; Sadun, Lorenzo; Weiss, Barak (2016)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
Avila, Artur; Bochi, Jairo; Damanik, David (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 ...