7 papers
Reducibility and Diagonal Equality Strata for Finite Jacobi Pencils
Matthew Faust
We study reducibility of the characteristic polynomials of a class of finite Jacobi pencils. We classify the diagonal equality patterns for which generic connected couplings yield…
Generic Irreducibility of Bloch Varieties for Periodic Graph Operators
Matthew Faust, Wencai Liu
We give a complete characterization of generic irreducibility for dispersion polynomials and Bloch varieties of periodic graph operators. More precisely, we prove that for a generi…
A counterexample to Fermi isospectral rigidity for two dimensional discrete periodic Schrödinger operators
Taylor Brysiewicz, Matthew Faust, Wencai Liu
Using numerical certification, we prove the existence of a nontrivial real-valued two dimensional periodic potential whose associated discrete Schrödinger operator is Fermi isospec…
Absence of flat bands for discrete periodic graph operators with generic potentials
Matthew Faust, Ilya Kachkovskiy
We show that Schrödinger-type operators on discrete connected periodic graphs do not have flat bands for generic potentials.
Rare Flat Bands for Periodic Graph Operators
Matthew Faust, Wencai Liu
As a corollary of our main results, we prove that for any connected -periodic graph, when edge weights and potentials are treated as variables, the corresponding peri…
Extrema of spectral band functions of two dimensional discrete periodic Schrödinger operators
Matthew Faust, Wencai Liu, Ethan Luo
We use Bézout's theorem and Bernstein-Khovanskii-Kushnirenko theorem to analyze the level sets of the extrema of the spectral band functions of discrete periodic Schrödinger operat…
Floquet Isospectrality of the Zero Potential for Discrete Periodic Schrödinger Operators
Matthew Faust, Wencai Liu, Rodrigo Matos +5
Let , with for each , and denote by the discrete Laplacian…