97-553 Kirsch W., Krishna M., Obermeit J.

Anderson Model with decaying randomness: Mobility Edge (36K, LATeX 2e) Oct 22, 97

Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

Abstract. \abstract{In this paper we consider the Anderson model with decaying randomness $a_nq_{\omega}(n)$, $a_n > 0, n \in \ZZ^{\nu}$ and $q_{\omega}(n)$, i.i.d random variables with an absolutely continuous distribution $\mu$. For a class of $\mu$ we show the following results on a set $\omega$ of full measure. (i) If $|a_n| \rightarrow 0$ as $|n| \rightarrow \infty$, then $\sigma_c(H_{\omega}) \subseteq [-2\nu, 2\nu]$ (ii) $\sigma(H_{\omega}) = \RR$. (iii) If $|a_n| \leq (|n|^{-1-\epsilon})$ for large $|n|$ and $\nu \geq 3$, the mobility edges are the two points $\{-2\nu, 2\nu\}$.

Files: 97-553.tex