Diffractive paths for weak localization in quantum billiards

TL;DR

This paper investigates the role of diffractive paths in weak localization within quantum billiards, showing that diffraction at lead mouths significantly influences conductance suppression and aligns semiclassical and quantum results.

Contribution

It identifies diffractively backscattered paths as key to weak localization in regular quantum billiards, providing a new semiclassical approach that matches quantum and experimental data.

Findings

Diffractive scattering couples transmission and reflection paths.

Semiclassical calculations with diffractive paths agree with quantum results.

The theory applies to systems with few open modes and mixed or chaotic dynamics.

Abstract

We study the weak localization effect in quantum transport through a clean ballistic cavity with regular classical dynamics. We address the question which paths account for the suppression of conductance through a system where disorder and chaos are absent. By exploiting both quantum and semiclassical methods, we unambiguously identify paths that are diffractively backscattered into the cavity (when approaching the lead mouths from the cavity interior) to play a key role. Diffractive scattering couples transmitted and reflected paths and is thus essential to reproduce the weak-localization peak in reflection and the corresponding anti-peak in transmission. A comparison of semiclassical calculations featuring these diffractive paths yields good agreement with full quantum calculations and experimental data. Our theory provides system-specific predictions for the quantum regime of few open lead modes and can be expected to be relevant also for mixed as well as chaotic systems.