10 citations · 20 across the 6 of their papers we have counts for
8 papers
Localization and Cantor spectrum for quasiperiodic discrete Schrödinger operators with asymmetric, smooth, cosine-like sampling functions
Yakir Forman, Tom VandenBoom
We prove Cantor spectrum and almost-sure Anderson localization for quasiperiodic discrete Schrödinger operators with potential sampled with Diophantine fr…
Finite-gap CMV matrices: Periodic coordinates and a Magic Formula
Jacob S. Christiansen, Benjamin Eichinger, Tom VandenBoom
We prove a bijective unitary correspondence between 1) the isospectral torus of almost-periodic, absolutely continuous CMV matrices having fixed finite-gap spectrum and 2) special…
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…
KdV hierarchy via Abelian coverings and operator identities
Benjamin Eichinger, Tom VandenBoom, Peter Yuditskii
We establish precise spectral criteria for potential functions of reflectionless Schrödinger operators to admit solutions to the Korteweg de-Vries (Kd…
Spectral Approximation for Ergodic CMV Operators with an Application to Quantum Walks
Jake Fillman, Darren C. Ong, Tom Vandenboom
We establish concrete criteria for fully supported absolutely continuous spectrum for ergodic CMV matrices and purely absolutely continuous spectrum for limit-periodic CMV matrices…
Localization for the one-dimensional Anderson model via positivity and large deviations for the Lyapunov exponent
Valmir Bucaj, David Damanik, Jake Fillman +4
We provide a complete and self-contained proof of spectral and dynamical localization for the one-dimensional Anderson model, starting from the positivity of the Lyapunov exponent…
Reflectionless discrete Schrödinger operators are spectrally atypical
Tom VandenBoom
We prove that, if an isospectral torus contains a discrete Schrödinger operator with nonconstant potential, the shift dynamics on that torus cannot be minimal. Consequently, we spe…
Almost Periodicity in Time of Solutions of the Toda Lattice
Ilia Binder, David Damanik, Milivoje Lukic +1
We study an initial value problem for the Toda lattice with almost periodic initial data. We consider initial data for which the associated Jacobi operator is absolutely continuous…