Jakšić-Last Theorem for Higher Rank Perturbations

Abstract

We consider the generalized Anderson Model $Δ+\sum_{n\in\mathcal{N}}ω_n P_n$, where $\mathcal{N}$ is a countable set, $\{ω_n\}_{n\in\mathcal{N}}$ are i.i.d random variables and $P_n$ are rank $N<\infty$ projections. For these models we prove theorem analogous to that of Jakšić-Last on the equivalence of the trace measure $σ_n(\cdot)=tr(P_nE_{H^ω}(\cdot)P_n)$ for $n\in\mathcal{N}$ a.e $ω$. Our model covers the dimer and polymer models.