# Effects of heterogeneity in site-site couplings for tight-binding models on scale-invariant structures

## TL;DR

This paper investigates how heterogeneity in site couplings affects thermodynamic properties of quantum gases on scale-invariant structures, revealing heterogeneity-dependent oscillations and conditions for Bose-Einstein condensation.

## Contribution

It analytically solves the energy spectrum of tight-binding models on scale-invariant structures and uncovers the impact of heterogeneity on thermodynamic behaviors.

## Key findings

- Log-periodic oscillations in specific heat depend on heterogeneity.
- Bose-Einstein condensation occurs only in non-homogeneous setups.
- Heterogeneity influences low-dimensional quantum phenomena.

## Abstract

We studied the thermodynamic behaviors of non-interacting bosons and fermions trapped by a scale-invariant branching structure of adjustable degree of heterogeneity. The full energy spectrum in tight-binding approximation was analytically solved . We found that the log-periodic oscillation of the specific heat for Fermi gas depended on the heterogeneity of hopping. Also, low dimensional Bose-Einstein condensation occurred only for non-homogeneous setup.