Connection between energy-spectrum self-similarity and specific heat log-periodicity

TL;DR

This paper investigates how self-similar energy spectra in quasiperiodic structures lead to log-periodic oscillations in specific heat, linking spectral scales to thermodynamic behavior through analytical and numerical methods.

Contribution

It introduces a novel analysis connecting fractal energy spectra with thermodynamic properties, specifically the log-periodic oscillations of specific heat.

Findings

Specific heat exhibits log-periodic oscillations at certain temperature ranges.

Scaling arguments relate oscillation features to spectral scales.

Analytical and numerical methods confirm the spectral-thermodynamic connection.

Abstract

As a first step towards the understanding of the thermodynamical properties of quasiperiodic structures, we have performed both analytical and numerical calculations associated with succesive hierarchical approximations to multiscale fractal energy spectra. We show that, in a certain range of temperatures, the specific heat displays log-periodic oscillations as a function of the temperature. We exhibit scaling arguments that allow for relating the mean value as well as the amplitude and period of the oscillations to the characteristic scales of the spectrum.