Isolated resonances in conductance fluctuations in ballistic billiards

TL;DR

This paper investigates isolated resonances in conductance fluctuations of ballistic billiards, linking them to eigenstates of the closed system and classifying these states based on phase space localization.

Contribution

It provides a detailed analysis connecting conductance resonances with eigenstates of the closed billiard, revealing their hierarchical or regular nature.

Findings

Resonances correspond to eigenstates of the closed system.

Resonances can be categorized as hierarchical or regular.

Conductance fluctuations are linked to phase space localization.

Abstract

We study the isolated resonances occurring in conductance fluctuations of ballistic electron systems with a classically mixed phase space. In particular, we calculate the conductance and Wigner-Smith time as well as scattering states and eigenstates of the open and closed cosine billiard, respectively. We demonstrate that the observed isolated resonances and their scattering states can be associated with eigenstates of the closed system. They can all be categorized as hierarchical or regular, depending on where in a phase space representation the corresponding eigenstates are concentrated.