What is the Thouless Energy for Ballistic Systems?

TL;DR

This paper investigates whether the Thouless energy remains relevant in ballistic systems and finds that it continues to characterize various thermodynamic observables despite the transition from diffusive to ballistic regimes.

Contribution

The study challenges the assumption that the Thouless energy becomes irrelevant in ballistic regimes, demonstrating its continued significance for thermodynamic quantities.

Findings

Thouless energy remains meaningful in ballistic systems.

Thermodynamic observables are still characterized by the Thouless energy.

Disorder-independent scales take over in the ballistic regime.

Abstract

The Thouless energy, $\Ec$ characterizes numerous quantities associated with sensitivity to boundary conditions in diffusive mesoscopic conductors. What happens to these quantities if the disorder strength is decreased and a transition to the ballistic regime takes place? In the present analysis we refute the intuitively plausible assumption that $\Ec$ loses its meaning as an inverse diffusion time through the system at hand, and generally disorder independent scales take over. Instead we find that a variety of (thermodynamic) observables are still characterized by the Thouless energy.