Аннотация:
In this talk I will tell about energy spectrum and energy-spacing distributions of
Hamitonians defined on fractal lattices. The first part of the talk is devoted to classical methods
of calculation of fractals spectra such as spectral decimation procedure and some estimates of
power-law behavior of energy-spacing distributions. The second part introduces a linearized
spectral decimation method. This approach provides qualitative explanation for various spectral
properties of self-similar graphs within the theory of dynamical systems, including the power-law level-spacing distribution, smooth density of states and effective chaotic regime.
