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math-ph2023
Flat bands of periodic graphs
Mostafa Sabri, Pierre Youssef
We study flat bands of periodic graphs in a Euclidean space. These are infinitely degenerate eigenvalues of the corresponding adjacency matrix, with eigenvectors of compact support…
math-ph2022
Quantum ergodicity for periodic graphs
Theo Mckenzie, Mostafa Sabri
We prove quantum ergodicity for a family of periodic Schrödinger operators on periodic graphs. This means that most eigenfunctions of on large finite periodic graphs are eq…