Fractality of wave functions on a Cayley tree: Difference between a tree and a locally tree-like graph without boundary
Disordered Systems and Neural Networks
2016-12-28 v1
Abstract
We investigate analytically and numerically eigenfunction statistics in a disordered system on a finite Bethe lattice (Cayley tree). We show that the wave function amplitude at the root of a tree is distributed fractally in a large part of the delocalized phase. The fractal exponents are expressed in terms of the decay rate and the velocity in a problem of propagation of a front between unstable and stable phases. We demonstrate a crucial difference between a loopless Cayley tree and a locally tree-like structure without a boundary (random regular graph) where extended wavefunctions are ergodic.
Keywords
Cite
@article{arxiv.1608.00331,
title = {Fractality of wave functions on a Cayley tree: Difference between a tree and a locally tree-like graph without boundary},
author = {K. S. Tikhonov and A. D. Mirlin},
journal= {arXiv preprint arXiv:1608.00331},
year = {2016}
}