Statistical Mechanics and Quantum Fields on Fractals

TL;DR

This paper explores how fractals' unique properties influence quantum field theory and statistical mechanics, focusing on heat kernels, spectral functions, and thermodynamics of fractal blackbodies, revealing new insights into dimensionality-dependent phenomena.

Contribution

It introduces the analysis of spectral properties and thermodynamics on fractals, highlighting their role as a testing ground for dimensionality effects in quantum physics.

Findings

Heat kernel behavior on fractals analyzed

Spectral zeta functions characterized for fractals

Thermodynamics of fractal blackbody studied

Abstract

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. Finally, we apply these results to specific problems such as thermodynamics of quantum radiation by a fractal blackbody.