Sharp bounds: Hausdorff spectral distance O(sqrt|delta|), edge/gap distances O(|delta|) for Weyl quantizations under singular symbol shifts.
Spectral Analysis of Quantum Hamiltonians
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Spectral butterflies form in parameter-dependent Schrödinger operators on weighted Delone sets and reflect fractal self-similar structures, with the framework extending across dimensions and to non-Abelian groups.
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Sharp spectral stability for a class of singularly perturbed pseudo-differential operators
Sharp bounds: Hausdorff spectral distance O(sqrt|delta|), edge/gap distances O(|delta|) for Weyl quantizations under singular symbol shifts.
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The butterflies' effects
Spectral butterflies form in parameter-dependent Schrödinger operators on weighted Delone sets and reflect fractal self-similar structures, with the framework extending across dimensions and to non-Abelian groups.