24 citations · 163 across the 51 of their papers we have counts for
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Measure of the spectra of periodic graph operators in the large-coupling limit
Jake Fillman
We derive a sharp criterion on the spectra of periodic discrete Schrödinger operators acting on connected periodic lattices: the measure of the spectrum goes to zero as the couplin…
Sharp Polynomial Velocity Decay Bounds for Multidimensional Periodic Schrödinger Operators
Houssam Abdul-Rahman, Jake Fillman, Christoph Fischbacher +1
We investigate periodic Schrödinger operators in arbitrary dimensions in the large coupling regime. Our results establish that both the Lieb--Robinson velocity and the asymptotic v…
Almost Periodic Solutions of The Cubic Defocusing Nonlinear Schrödinger Equation
Jake Fillman, Long Li, Milivoje Lukić +1
This paper addresses the Cauchy problem for the cubic defocusing nonlinear Schrödinger equation (NLS) with almost periodic initial data. We prove that for small analytic quasiperio…
Optimal dispersion for discrete periodic Schrödinger operators
David Damanik, Jake Fillman, Giorgio Young
We prove a dispersive estimate for periodic discrete Schrödinger operators on the line with optimal rate of decay. Additionally, by standard methods, we deduce dispersive estimates…
On the Spectra of Sieved Schrödinger Operators
Jake Fillman, Alexandro Luna
We give a family of examples of discrete Schrödinger operators whose spectral dimension is not invariant under sieving. The examples are produced from the Fibonacci Hamiltonian, wh…
Thin Spectra for Periodic and Ergodic Word Models
Jake Fillman, Michala N. Gradner, Hannah J. Hendricks
We establish a new and simple criterion that suffices to generate many spectral gaps for periodic word models. This leads to new examples of ergodic Schrödinger operators with Cant…