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arXiv · 1608.00331

Fractality of wave functions on a Cayley tree: Difference between a tree and a locally tree-like graph without boundary

K. S. Tikhonov·A. D. Mirlin
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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.

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K. S. Tikhonov, A. D. Mirlin. 2016-08-01. Fractality of wave functions on a Cayley tree: Difference between a tree and a locally tree-like graph without boundary. https://doi.org/10.1103/physrevb.94.184203

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