Isolated resonances in conductance fluctuations in ballistic billiards

TL;DR

This paper investigates quantum conductance fluctuations in ballistic billiards with mixed phase space, revealing isolated resonances linked to classical phase space structures and classifying resonant states accordingly.

Contribution

It provides a detailed numerical analysis connecting quantum resonances to classical phase space structures, highlighting the origin of isolated resonances in mixed systems.

Findings

Isolated resonances with broad width distribution observed in conductance and Wigner delay time.

A one-to-one correspondence established between resonant scattering states and eigenstates of the closed system.

Resonant states classified into regular and hierarchical based on phase space Husimi representations.

Abstract

We study numerically quantum transport through a billiard with a classically mixed phase space. In particular, we calculate the conductance and Wigner delay time by employing a recursive Green's function method. We find sharp, isolated resonances with a broad distribution of resonance widths in both the conductance and the Wigner time, in contrast to the well-known smooth conductance fluctuations of completely chaotic billiards. In order to elucidate the origin of the isolated resonances, we calculate the associated scattering states as well as the eigenstates of the corresponding closed system. As a result, we find a one-to-one correspondence between the resonant scattering states and eigenstates of the closed system. The broad distribution of resonance widths is traced to the structure of the classical phase space. Husimi representations of the resonant scattering states show a strong overlap either with the regular regions in phase space or with the hierarchical parts surrounding the regular regions. We are thus lead to a classification of the resonant states into regular and hierarchical, depending on their phase space portrait.