Revisiting Thouless conductance formula

TL;DR

This paper presents an alternative derivation of the Thouless energy scaling with conductance in 1-D systems, differing from previous perturbation theory results, and verifies findings through numerical calculations.

Contribution

It introduces a new derivation method for Thouless energy scaling in 1-D systems and discusses its potential applicability to higher dimensions.

Findings

Thouless energy scales differently with conductance than previously thought

The new derivation aligns with numerical results

Results suggest possible extension to higher-dimensional systems

Abstract

It was shown using perturbation theory[1] that Thouless energy Ec for a quantum system scales linearly with the conductance of the system. We derive in an alternate way in 1-D that Ec scales with the conductance in a very different way. We physically show the difference between our approach and that of ref. 1 to expect our results to hold in higher dimensions also. We verify our results with exact numerical calculations.