Faculty & Staff Researchhttp://hdl.handle.net/1911/751722019-08-23T22:44:19Z2019-08-23T22:44:19ZAnderson localization for quasi-periodic CMV matrices and quantum walksWang, FengpengDamanik, Davidhttp://hdl.handle.net/1911/1062732019-08-22T08:11:42Z2019-01-01T00:00:00ZAnderson localization for quasi-periodic CMV matrices and quantum walks
Wang, Fengpeng; Damanik, David
We consider CMV matrices, both standard and extended, with analytic quasi-periodic Verblunsky coefficients and prove Anderson localization in the regime of positive Lyapunov exponents. This establishes the CMV analog of a result Bourgain and Goldstein proved for discrete one-dimensional Schrödinger operators. We also prove a similar result for quantum walks on the integer lattice with suitable analytic quasi-periodic coins.
2019-01-01T00:00:00ZAnderson localization for radial tree graphs with random branching numbersDamanik, DavidSukhtaiev, Selimhttp://hdl.handle.net/1911/1062722019-08-22T08:11:40Z2019-01-01T00:00:00ZAnderson localization for radial tree graphs with random branching numbers
Damanik, David; Sukhtaiev, Selim
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 half-lineﾠJacobi matricesﾠwhose entries are non-degenerate, independent, identically distributed random variables with singular distributions.
2019-01-01T00:00:00ZLimit-periodic Schrödinger operators with Lipschitz continuous IDSDamanik, DavidFillman, Jakehttp://hdl.handle.net/1911/1062712019-08-22T08:11:38Z2019-01-01T00:00:00ZLimit-periodic Schrödinger operators with Lipschitz continuous IDS
Damanik, David; Fillman, Jake
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.
2019-01-01T00:00:00ZMultidimensional Almost-Periodic Schrödinger Operators with Cantor SpectrumDamanik, DavidFillman, JakeGorodetski, Antonhttp://hdl.handle.net/1911/1062742019-08-22T08:11:45Z2019-01-01T00:00:00ZMultidimensional Almost-Periodic Schrödinger Operators with Cantor Spectrum
Damanik, David; Fillman, Jake; Gorodetski, Anton
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.
2019-01-01T00:00:00Z