24 citations · 163 across the 51 of their papers we have counts for
5 papers · 1 filter
Singular continuous Cantor spectrum for magnetic quantum walks
C. Cedzich, J. Fillman, T. Geib +1
In this note, we consider a physical system given by a two-dimensional quantum walk in an external magnetic field. In this setup, we show that both the topological structure as wel…
Ergodic Schrödinger Operators in the Infinite Measure Setting
Michael Boshernitzan, David Damanik, Jake Fillman +1
We develop the basic theory of ergodic Schrödinger operators, which is well known for ergodic probability measures, in the case of a base dynamics on an infinite measure space. Thi…
Random Hamiltonians with Arbitrary Point Interactions
David Damanik, Jake Fillman, Mark Helman +2
We consider disordered Hamiltonians given by the Laplace operator subject to arbitrary random self-adjoint singular perturbations supported on random discrete subsets of the real l…
Positive Lyapunov Exponents and a Large Deviation Theorem for Continuum Anderson Models, Briefly
Valmir Bucaj, David Damanik, Jake Fillman +4
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 m…
Localization for Anderson Models on Metric and Discrete Tree Graphs
David Damanik, Jake Fillman, Selim Sukhtaiev
We establish spectral and dynamical localization for several Anderson models on metric and discrete radial trees. The localization results are obtained on compact intervals contain…