Crystalline conductance and absolutely continuous spectrum of 1D samples

TL;DR

This paper links the absolutely continuous spectrum of 1D Schrödinger operators to the limiting behavior of crystalline conductance in finite samples, providing a spectral characterization.

Contribution

It introduces a novel characterization of the absolutely continuous spectrum using the limiting crystalline Landauer-Büttiker conductance for 1D Schrödinger operators.

Findings

Characterizes the absolutely continuous spectrum via conductance limits

Establishes a connection between spectral properties and transport measures

Provides a new spectral criterion based on finite sample conductance

Abstract

We characterize the absolutely continuous spectrum of half-line one-dimensional Schr\"odinger operators in terms of the limiting behavior of the Crystaline Landauer-B\"uttiker conductance of the associated finite samples.