Thermodynamical fingerprints of fractal spectra

TL;DR

This paper explores how fractal spectra influence thermodynamic properties, revealing log-periodic oscillations in specific heats linked to spectral self-similarity, with implications for substitutional and hierarchical structures.

Contribution

It provides analytical and numerical insights into the thermodynamics of systems with fractal spectra, highlighting the role of self-similarity in thermodynamic oscillations.

Findings

Log-periodic oscillations in specific heat due to spectral self-similarity

Average specific heat relates to the power law density of states

Regularities in electronic thermodynamics for special cases

Abstract

We investigate the thermodynamics of model systems exhibiting two-scale fractal spectra. In particular, we present both analytical and numerical studies on the temperature dependence of the vibrational and electronic specific heats. For phonons, and for bosons in general, we show that the average specific heat can be associated to the average (power law) density of states. The corrections to this average behavior are log-periodic oscillations which can be traced back to the self-similarity of the spectral staircase. In the electronic case, even if the thermodynamical quantities exhibit a strong dependence on the particle number, regularities arise when special cases are considered. Applications to substitutional and hierarchical structures are discussed.