24 citations · 163 across the 51 of their papers we have counts for
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Spectral Characteristics of the Unitary Critical Almost-Mathieu Operator
Jake Fillman, Darren C. Ong, Zhenghe Zhang
We discuss spectral characteristics of a one-dimensional quantum walk whose coins are distributed quasi-periodically. The unitary update rule of this quantum walk shares many spect…
Limit-Periodic Continuum Schrödinger Operators with Zero Measure Cantor Spectrum
David Damanik, Jake Fillman, Milivoje Lukic
We consider Schrödinger operators on the real line with limit-periodic potentials and show that, generically, the spectrum is a Cantor set of zero Lebesgue measure and all spectral…
Purely Singular Continuous Spectrum for Sturmian CMV Matrices via Strengthened Gordon Lemmas
Jake Fillman
The Gordon Lemma refers to a class of results in spectral theory which prove that strong local repetitions in the structure of an operator preclude the existence of eigenvalues for…
Quantum Intermittency for Sparse CMV Matrices with an Application to Quantum Walks on the Half-Line
David Damanik, Jon Erickson, Jake Fillman +2
We study the dynamics given by the iteration of a (half-line) CMV matrix with sparse, high barriers. Using an approach of Tcheremchantsev, we are able to explicitly compute the tra…
Spreading Estimates for Quantum Walks on the Integer Lattice via Power-Law Bounds on Transfer Matrices
David Damanik, Jake Fillman, Darren C. Ong
We discuss spreading estimates for dynamical systems given by the iteration of an extended CMV matrix. Using a connection due to Cantero--Grünbaum--Moral--Velázquez, this enables u…
Mixed spectral regimes for square Fibonacci Hamiltonians
Jake Fillman, Yuki Takahashi, William Yessen
For the square tridiagonal Fibonacci Hamiltonian, we prove existence of an open set of parameters which yield mixed interval-Cantor spectra (i.e. spectra containing an interval as…
Spectral Homogeneity of Limit-Periodic Schrödinger Operators
Jake Fillman, Milivoje Lukic
We prove that the spectrum of a limit-periodic Schrödinger operator is homogeneous in the sense of Carleson whenever the potential obeys the Pastur--Tkachenko condition. This impli…