Heat Kernels and Zeta Functions on Fractals

TL;DR

This paper explores the unique behaviors of spectral functions like heat kernels and zeta functions on fractals, highlighting their significant implications for classical and quantum physics in fractal systems.

Contribution

It provides a detailed analysis of spectral functions on fractals, revealing features distinct from smooth manifolds and their physical relevance.

Findings

Spectral functions on fractals show novel behaviors.

These behaviors differ markedly from those on smooth manifolds.

Implications for physics in fractal systems are significant.

Abstract

On fractals, spectral functions such as heat kernels and zeta functions exhibit novel features, very different from their behaviour on regular smooth manifolds, and these can have important physical consequences for both classical and quantum physics in systems having fractal properties.