Smoothness of the integrated density of states on strips
The smoothness of the integrated density of states k(E) of a random Schrödinger operator on a discrete strip lattice is investigated. It is proved that k(E) is \(C^{\infty}\), if the potentials on the top surface of the strip have distributions with compactly supported densities in some fractional order Sobolev space. The \(C^{\infty}\)-result for the case that all potentials have a distribution with compactly supported density in some Sobolev space (i.e. the Anderson model), is also recovered.
scientific article; zbMATH DE number 4161276
scientific article