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Spectral Properties of Schrödinger Operators on Perturbed Lattices (1408.2076v2)
Published 9 Aug 2014 in math.SP, math-ph, math.AP, and math.MP
Abstract: We study the spectral properties of Schr\"{o}dinger 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.