Now showing items 1-3 of 3
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.
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.
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 ...