24 citations · 163 across the 51 of their papers we have counts for
64 papers
Learned Control Variates for Rare Grid-Outage Estimation at Electric Vehicle Charging Stations
Sulyman Iyanda, Mansur Arief
Public charging of electric vehicles (EVs) adds a large and synchronized load to the distribution feeders. In most networks, it is rare to overload a feeder at the same time. When…
On the identification of certain classes of gap-rich sets
Jake Fillman, Yi-Sheng Lim
The notion of gap-richness was recently introduced to quantify the ability to open spectral gaps for periodic word models by arbitrarily small perturbations and is useful in the co…
Continuum Fibonacci Schrödinger Operators in the Strongly Coupled Regime
David Damanik, Mark Embree, Jake Fillman +2
We study Schrödinger operators on the real line whose potentials are generated by the Fibonacci substitution sequence and a rule that replaces symbols by compactly supported potent…
Absence of ballistic motion and presence of almost-ballistic motion for unitary operators with pure point spectrum
Christopher Cedzich, Jake Fillman, Luis Velázquez
We adapt two results of Simon and collaborators to the setting of discrete-time unitary dynamics. We show that pure point spectrum precludes ballistic motion, and exhibit a family…
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…
Gap Labels and Asymptotic Gap Opening for Full Shifts
David Damanik, Íris Emilsdóttir, Jake Fillman
We discuss gap labelling for operators generated by the full shift over a compact subset of the real line. The set of Johnson--Schwartzman gap labels is the algebra generated by we…
Mobility edges in pseudo-unitary quasiperiodic quantum walks
Christopher Cedzich, Jake Fillman
We introduce a Floquet quasicrystal that simulates the motion of Bloch electrons in a homogeneous magnetic field in discrete time steps. We admit the hopping to be non-reciprocal w…
Computing Spectral Size: Rigorous Algorithms and the Limits of Computation
Matthew J. Colbrook, Mark Embree, Jake Fillman
Many structures in mathematical physics and dynamics exhibit intricate fractal geometry. Such behavior appears prominently in quantum mechanics and materials science through spectr…
Absence of Bound States for Quantum Walks and CMV Matrices via Reflections
Christopher Cedzich, Jake Fillman
We give a criterion based on reflection symmetries in the spirit of Jitomirskaya--Simon to show absence of point spectrum for (split-step) quantum walks and Cantero--Moral--Velázqu…
On the Number of Closed Gaps of Discrete Periodic One-Dimensional Operators
Andrew Arroyo, Faye Castro, Jake Fillman
From the general inverse theory of periodic Jacobi matrices, it is known that a periodic Jacobi matrix of minimal period may have at most closed spectral gaps. We…
Exact mobility edges for almost-periodic CMV matrices via gauge symmetries
Christopher Cedzich, Jake Fillman, Long Li +2
We investigate the symmetries of so-called generalized extended CMV matrices. It is well-documented that problems involving reflection symmetries of standard extended CMV matrices…
Algebraic Properties of the Fermi Variety for Periodic Graph Operators
Jake Fillman, Wencai Liu, Rodrigo Matos
We present a method to estimate the number of irreducible components of the Fermi varieties of periodic Schrödinger operators on graphs in terms of suitable asymptotics. Our main t…
The Schwartzman Group of an Affine Transformation
David Damanik, Íris Emilsdóttir, Jake Fillman
We compute the Schwartzman group associated with an ergodic affine automorphism of a compact connected abelian group given by the composition of an automorphism of the group and a…
Gap Labels for Zeros of the Partition Function of the 1D Ising Model via the Schwartzman Homomorphism
David Damanik, Mark Embree, Jake Fillman
Inspired by the 1995 paper of Baake--Grimm--Pisani, we aim to explain the empirical observation that the distribution of Lee--Yang zeros corresponding to a one-dimensional Ising mo…
Discontinuities of the Integrated Density of States for Laplacians Associated with Penrose and Ammann-Beenker Tilings
David Damanik, Mark Embree, Jake Fillman +1
Aperiodic substitution tilings provide popular models for quasicrystals, materials exhibiting aperiodic order. We study the graph Laplacian associated with four tilings from the mu…
Johnson-Schwartzman Gap Labelling for Ergodic Jacobi Matrices
David Damanik, Jake Fillman, Zhenghe Zhang
We consider two-sided Jacobi matrices whose coefficients are obtained by continuous sampling along the orbits of a homeomorphim of a compact metric space. Given an ergodic probabil…
On Sums of Semibounded Cantor Sets
Jake Fillman, Sara H. Tidwell
Motivated by questions arising in the study of the spectral theory of models of aperiodic order, we investigate sums of functions of semibounded closed subsets of the real line. We…
The Almost Sure Essential Spectrum of the Doubling Map Model is Connected
David Damanik, Jake Fillman
We consider discrete Schrödinger operators on the half line with potentials generated by the doubling map and continuous sampling functions. We show that the essential spectrum of…
Limit-Periodic Dirac Operators with Thin Spectra
Benjamin Eichinger, Jake Fillman, Ethan Gwaltney +1
We prove that limit-periodic Dirac operators generically have spectra of zero Lebesgue measure and that a dense set of them have spectra of zero Hausdorff dimension. The proof comb…