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Extended States in the Anderson Model on the Bethe Lattice

✍ Scribed by Abel Klein

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
394 KB
Volume
133
Category
Article
ISSN
0001-8708

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✦ Synopsis

We prove that the Anderson Hamiltonian H * =&2+*V on the Bethe lattice has ``extended states'' for small disorder. More precisely, given any closed interval I contained in the interior of the spectrum of the Laplacian on the Bethe lattice, we prove that for small disorder H * has purely absolutely continuous spectrum in I with probability one (i.e., _ ac (H * ) & I=I and _ pp (H * ) & I=_ sc (H * ) & I=< with probability one), and its integrated density of states is continuously differentiable on the interval I.

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