Some spectral properties of fractal graphs

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.