Fig. 7: Localization on fractal lattice.
After preparing the system initially in the lower left corner of a G(7) Sierpiński gasket or the corresponding regular triangle, we plot in (a) the weight of the wave function within the lower-leftmost G(i) structure (as indicated in (b)). In the regular lattice the weight decays quickly and thermalizes at the thin dashed lines, corresponding to the ratio of site numbers Ns[G(i)]/Ns[(G7)]. In contrast, the weight in the fractal (solid lines), will always keep some memory of the initial state. J is the hopping term between each connected site.
