Mesoscopic System: Semiclassical vs Quantum

TL;DR

This paper explores the relationship between semiclassical and quantum descriptions of mesoscopic systems, focusing on Friedel sum rule formulas and their limitations in the presence of Fano resonances.

Contribution

It introduces a hierarchy of Friedel sum rule formulas and discusses the challenges in defining a physically relevant semiclassical limit for mesoscopic systems.

Findings

Quantum derivation of Friedel sum rule formulas

Identification of limitations due to Fano resonances

Highlighting the need for further research on semiclassical limits

Abstract

We explain a hierarchy of Friedel sum rule like formulas that help us understand response of mesoscopic systems to applied electric and magnetic fields. The formulas can be derived fully quantum mechanically and then there is a mathematical way to argue a semiclassical limit which may make the formulas practically relevant. But the mathematical prescription is not physically relevant in presence of a Fano resonance. A proper understanding of what exactly is the physical semiclassical limit is therefor not known and require future work.