Fermi-Edge Singularities in the Mesoscopic X-Ray Edge Problem

TL;DR

This paper investigates how mesoscopic fluctuations in chaotic quantum dots alter the x-ray edge problem, revealing a transition from rounded to peaked absorption edges as system size decreases.

Contribution

It demonstrates that mesoscopic effects significantly modify the x-ray edge singularity, changing the absorption edge shape in chaotic quantum systems at small scales.

Findings

Rounded edges in bulk become slightly peaked at mesoscopic scales.

Mesoscopic fluctuations cause substantial deviations from bulk x-ray absorption behavior.

The shape of the absorption edge depends on system size and coherence.

Abstract

We study the x-ray edge problem for a chaotic quantum dot or nanoparticle displaying mesoscopic fluctuations. In the bulk, x-ray physics is known to produce deviations from the naively expected photoabsorption cross section in the form of a peaked or rounded edge. For a coherent system with chaotic dynamics, we find substantial changes and in particular that a photoabsorption cross section showing a rounded edge in the bulk will change to a slightly peaked edge on average as the system size is reduced to a mesoscopic (coherent) scale.