Statistical Mechanics and Quantum Fields on Fractals

Understand

Fractals define a new and interesting realm for a discussion of basic phenomena in quantum field theory and statistical mechanics.

• This interest results from specific properties of fractals, e.g., their dilatation symmetry and the corresponding absence of Fourier mode decomposition.
• Moreover, the existence of a set of distinct dimensions characterizing the physical properties (spatial or spectral) of fractals make them a useful testing ground for dimensionality dependent physical problems.
• This paper addresses specific problems including the behavior of the heat kernel and spectral zeta functions on fractals and their importance in the expression of spectral properties in quantum physics.