4 papers · 1 filter
Singular continuous spectrum and generic full spectral/packing dimension for unbounded quasiperiodic Schrödinger operators
Fan Yang, Shiwen Zhang
We proved that Schrödinger operators with unbounded potentials have purely singular continuous spectrum on the set $\{E:…
Spectral Dimension for -almost periodic singular Jacobi operators and the extended Harper's model
Rui Han, Fan Yang, Shiwen Zhang
We study fractal dimension properties of singular Jacobi operators. We prove quantitative lower spectral/quantum dynamical bounds for general operators with strong repetition prope…
Large deviation estimates and Hölder regularity of the Lyapunov exponents for quasi-periodic Schrödinger cocycles
Rui Han, Shiwen Zhang
We consider one-dimensional quasi-periodic Schrödinger operators with analytic potentials. In the positive Lyapunov exponent regime, we prove large deviation estimates which lead t…
The exact Power Law for Buffon's needle landing near some Random Cantor Sets
Shiwen Zhang
In this paper, we study the Favard length of some random Cantor sets of Hausdorff dimension 1. We start with a unit disk in the plane and replace the unit disk by disjoint subd…