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Long-range scattering theory for discrete Schrödinger operators on graphene (1811.11527v3)
Published 28 Nov 2018 in math-ph, math.MP, and math.SP
Abstract: We consider a long-range scattering theory for discrete Schr\"odinger operators on the hexagonal lattice, which describe tight-binding Hamiltonians on the graphene sheet. We construct Isozaki-Kitada modifiers for a pair of the difference Laplacian on the hexagonal lattice and perturbed operators with long-range potentials. We prove that these modified wave operators exist and that they are asymptotically complete.