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Absolute Continuity of the Spectrum of Coupled Identical Systems on 1D Lattices

  • B. LangellaEmail author
  • D. BambusiEmail author
Article

Abstract

We prove that the spectrum of the discrete Schrödinger operator on 2(2)
$$\begin{array}{@{}rcl@{}} (\psi _{n,m})\mapsto -(\psi _{n + 1,m} +\psi _{n-1,m} + \psi _{n,m + 1} +\psi _{n,m-1})+V_{n}\psi _{n,m} \ , \\ \quad (n, m) \in \mathbb {Z}^{2},\ \left \{ V_{n}\right \}\in \ell ^{\infty }(\mathbb {Z}) \end{array} $$
(1)
is absolutely continuous.

Notes

Acknowledgments

We thank Didier Robert for pointing to our attention the paper [5].

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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità degli Studi di MilanoMilanoItaly

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