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• W2607921126 abstract "A one-channel operator is a self-adjoint operator on $ell^2(mathbb{G})$ for some countable set $mathbb{G}$ with a rank 1 transition structure along the sets of a quasi-spherical partition of $mathbb{G}$. Jacobi operators are a very special case. In essence, there is only one channel through which waves can travel across the shells to infinity. This channel can be described with transfer matrices which include scattering terms within the shells and connections to neighboring shells. Not all of the transfer matrices are defined for some countable set of energies. Still, many theorems from the world of Jacobi operators are translated to this setup. The results are then used to show absolutely continuous spectrum for the Anderson model on certain finite dimensional graphs with a one-channel structure. This result generalizes some previously obtained results on antitrees." @default.
• W2607921126 created "2017-05-05" @default.
• W2607921126 creator A5005645997 @default.
• W2607921126 date "2018-04-01" @default.
• W2607921126 modified "2023-09-29" @default.
• W2607921126 title "Spectral theory of one-channel operators and application to absolutely continuous spectrum for Anderson type models" @default.
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• W2607921126 doi "https://doi.org/10.1016/j.jfa.2018.01.017" @default.
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