Negative partial density of states in mesoscopic systems

TL;DR

This paper investigates the possibility of negative partial density of states in mesoscopic systems, using Argand diagrams and Burgers circuits to address unresolved theoretical issues related to quantum scattering phases.

Contribution

It provides the first general proof of negative partial density of states in mesoscopic systems and classifies scattering matrix behaviors based on Argand diagram topology.

Findings

Negative partial density of states can occur in mesoscopic systems.

A connection between phase drops and Friedel sum rule accuracy is established.

Argand diagrams classify scattering matrix behaviors.

Abstract

Since the experimental observation of quantum mechanical scattering phase shift in mesoscopic systems, several aspects of it has not yet been understood. The experimental observations has also accentuated many theoretical problems related to Friedel sum rule and negativity of partial density of states. We address these problems using the concepts of Argand diagram and Burgers circuit. We can prove the possibility of negative partial density of states in mesoscopic systems. Such a conclusive and general evidence cannot be given in one, two or three dimensions. We can show a general connection between phase drops and exactness of semi classical Friedel sum rule. We also show Argand diagram for a scattering matrix element can be of few classes based on their topology and all observations can be classified accordingly.