Cayley tree self-energy

Figure 64. Schematic of a self-similar structure potential energy landscape and of the Cayley tree.

We remark that the self-similar potential energy landscape (Fig. 68) resembles a Cayley tree (Fig. 68), provided each minimum at a certain self-... 

Figure 4 Schematic illustration of self-consistent solution for Amp, the most probable value of imaginary part of the self-energy. The dashed lines indicated the dependence of the most probable value at level j in the Cayley tree on the most probable value at the next level k. -p is the dephasing rate. The self-consistent value of Amp is obtained from the intersection with the solid line. For many overlapping resonances, when the Thouless number g appearing in Figure 1 is large, this yields a finite, nonvanishing value, even for vanishing t). However, there are few overlapping resonances, when the Thouless number g is small, the intersection occurs for a value that vanishes as - 0.

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