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Lenses make many points: Pure point spectrum disproves Simon's conjecture
Simon Becker, Mengxuan Yang
For every and , we construct with LLM-assistance a smooth bounded nonnegative lens-type potential with arbitrarily small $\|V\|_\infty+\int_{\mathbb{R}^d}|x|…
Counterexamples to the ordinary Fried conjecture near hyperbolic metrics
Simon Becker, Benjamin Lawton
We give an LLM-assisted construction of counterexamples to the ordinary Fried conjecture, with real analytic metrics arbitrarily close to a hyperbolic metric in dimension three. Fo…
On optimal Wannier decay in dimension three
Simon Becker, Zhongkai Tao, Mengxuan Yang
For a Chern nontrivial Bloch bundle over the three torus, we construct an orthonormal Wannier basis with the optimal pointwise decay . All but one of the g…
Don't mind the gap: Absolutely Continuous Edge Spectrum in a Mobility Gap
Simon Becker, Mengxuan Yang
We study the edge spectrum of two-dimensional lattice Hamiltonians and magnetic Schrödinger operators in a mobility gap, an energy interval in which the bulk spectrum is potentiall…