Mittwoch, 13.05.2015: Anderson transition at two dimensional growth rate for antitrees with normalized edge weights
Dr. Christian Sadel (IST WIen)
An antitree is a graph $\mathbb{G}$ consisting of shells $S_n, n\geq 0$ which contain finitely many vertices, such that each vertex in $S_n$ is connected with each vertex in $S_{n+1}$ by an edge. There are no further edges. We are particularly interested in the case where the number of vertices in $S_n$ grows polynomially like $n^{d-1}$ which corresponds to a $d$-dimensional growth rate. The growth is uniform, if $\lim \#(S_n) / n^{d-1}=c>0$ exists.
We normalize the edges to get a bounded adjacency operator $A$ and consider the Anderson model $A+V$ where $V$ is a random, i.i.d. potential. In a certain set $I$ of energies and for uniformly $d$-dimensional growth rates, we obtain a transition in the type of the spectrum from pure point ($d<2$) to partly pure point and partly singular continuous $d=2$) to absolutely continuous $d>2$).
| Uhrzeit: |
16:15 |
| Ort: |
TBA |
| Gruppe: |
Oberseminar Mathematische Physik |
| Einladender: |
Hainzl, Keppeler, Teufel |
