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Article Dans Une Revue Communications in Mathematical Physics Année : 2021

Absolutely Continuous Spectrum for Quantum Trees

Mostafa Sabri
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Résumé

We study the spectra of quantum trees of finite cone type. These are quantum graphs whose geometry has a certain homogeneity, and which carry a finite set of edge lengths, coupling constants and potentials on the edges. We show the spectrum consists of bands of purely absolutely continuous spectrum, along with a discrete set of eigenvalues. Afterwards, we study random perturbations of such trees, at the level of edge length and coupling, and prove the stability of pure AC spectrum, along with resolvent estimates.
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Dates et versions

hal-02523082 , version 1 (28-03-2020)

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  • HAL Id : hal-02523082 , version 1

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Nalini Anantharaman, Maxime Ingremeau, Mostafa Sabri, Brian Winn. Absolutely Continuous Spectrum for Quantum Trees. Communications in Mathematical Physics, 2021, 383, pp.537-594. ⟨hal-02523082⟩
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