Cayley树上波函数的分形性：树与无边界局部树型图的区别
Fractality of wave functions on a Cayley tree: Difference between a tree and a locally tree-like graph without boundary
摘要：
本文研究了有限Bethe格点（Cayley树）上无序系统的本征函数统计特性。我们表明，在树的根部的波函数振幅分布分形在离域相位的很大一部分。分形指数表示的衰减率和速度在不稳定和稳定阶段之间的前沿传播的问题。我们证明了一个无环凯莱树和一个局部树状结构没有边界（随机正则图），其中扩展的波函数是遍历的一个重要区别。
英文摘要：
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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