8 research outputs found
Absolutely Continuous Spectrum for Random Schroedinger Operators on the Bethe Strip
The Bethe Strip of width is the cartesian product \B\times\{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_\lambda=\frac12 \Delta \otimes 1 + 1
\otimes A + \lambda \Vv on a Bethe strip with connectivity , where
is an symmetric matrix, \Vv is a random matrix potential, and
is the disorder parameter. Given any closed interval , where
and are the smallest and largest
eigenvalues of the matrix , we prove that for small the random
Schr\"odinger operator has purely absolutely continuous spectrum
in with probability one and its integrated density of states is
continuously differentiable on the interval
Regularity of the density of states in the Anderson model on a strip for potentials with singular continuous distributions
We derive regularity properties for the density of states in the Anderson model on a one-dimensional strip for potentials with singular continuous distributions. For example, if the characteristic function is infinitely differentiable with bounded derivatives and together with all its derivatives goes to zero at infinity, we show that the density of states is infinitely differentiable.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45156/1/10955_2005_Article_BF01023635.pd