Abstract
We study the spectral properties of Schrödinger operators on perturbed lattices. We shall prove the non-existence or the discreteness of embedded eigenvalues, the limiting absorption principle for the resolvent, construct a spectral representation, and define the S-matrix. Our theory covers the square, triangular, diamond, Kagome lattices, as well as the ladder, the graphite and the subdivision of square lattice.
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Communicated by Jan Dereziński.
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Ando, K., Isozaki, H. & Morioka, H. Spectral Properties of Schrödinger Operators on Perturbed Lattices. Ann. Henri Poincaré 17, 2103–2171 (2016). https://doi.org/10.1007/s00023-015-0430-0
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DOI: https://doi.org/10.1007/s00023-015-0430-0