We give a new proof of a version of Klein's theorem on the existence of absolutely continuous spectrum for the Anderson model on the Bethe Lattice at weak disorder.
Model and Statement of Main ResultsIt is widely believed that the Anderson model [An] should exhibit absolutely continuous spectrum at weak disorder in dimensions three and higher. But it is only for the Bethe lattice B,
A new class of sum rules in nonrelativistic scattering theory is obtained. By extending the concept of the Fredholm determinant to a local form defined at each space point *, a function with analytic properties analogous to the Fredholm determinant, but containing more information, is found. These rules assume the form of the power-moment problem and are valid in both quantum and classical mechanics.
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