Contents: (Math. Nachr. 1/2012)

• Book ID: 102496898
• Publisher: John Wiley and Sons
• Year: 2011
• Tongue: English
• Weight: 89 KB
• Volume: 285
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.201210401

✦ Synopsis

The Bethe strip of width m is the cartesian product B × {1, . . . , m}, where B is the Bethe lattice (Cayley tree). We prove that Anderson models on the Bethe strip have "extended states" for small disorder. More precisely, we consider Anderson-like Hamiltonians H λ = 1 2 Δ ⊗ 1 + 1 ⊗ A + λV on a Bethe strip with connectivity K ≥ 2, where A is an m × m symmetric matrix, V is a random matrix potential, and λ is the disorder parameter. Given any closed interval I ⊂ (-

, where a min and a max are the smallest and largest eigenvalues of the matrix A, we prove that for λ small the random Schrödinger operator H λ has purely absolutely continuous spectrum in I with probability one and its integrated density of states is continuously differentiable on the interval I.