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- W2108509054 abstract "We discuss two types of defects in two-dimensional lattices, namely (1) translational dislocations and (2) defects roduced by a rotation of the lattice in a half-space. For Lipschitz-continuous and ℤ2-periodic potentials, we first show that translational dislocations produce spectrum inside the gaps of the periodic problem; we also give estimates for the (integrated) density of the associated surface states.W e then study lattices with a small angle defect where we find that the gaps of the periodic problem fill with spectrum as the defect angle goes to zero.T o introduce our methods, we begin with the study of dislocation problems on the real line and on an infinite strip.F inally, we consider examples of muffin tin type.O ur overview refers to results in [HK1, HK2]." @default.
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- W2108509054 date "2012-01-01" @default.
- W2108509054 modified "2023-10-02" @default.
- W2108509054 title "Dislocation Problems for Periodic Schrödinger Operators and Mathematical Aspects of Small Angle Grain Boundaries" @default.
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- W2108509054 doi "https://doi.org/10.1007/978-3-0348-0297-0_23" @default.
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