Two Dimensional Magnetic Schrödinger Operators: Width of Mini Bands in the Tight Binding Approximation
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The spectral properties of two dimensional magnetic Schrödinger operators are studied. It is shown in the tight-binding limit that when a nonzero constant magnetic field is perturbed by an infinite number of magnetic and scalar "wells", the essential spectrum continues to have gaps and moreover, it can be nonempty in between the Landau levels and is localized near the one well Hamiltonian eigenvalues which develop into mini-bands whose width is believed to be optimally controlled.
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