Diffractive paths for weak localization in quantum billiards

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.

5 pages, 3 figures, final version with extended discussion and added references

References in corpus (6)

• Semiclassical Theory of Chaotic Conductors
• Localization of Matter Waves in 2D-Disordered Optical Potentials
• Ballistic quantum transport at high energies and high magnetic fields
• Shot noise in the chaotic-to-regular crossover regime
• Pseudo-Path Semiclassical Approximation to Transport through Open Quantum Billiards: Dyson Equation for Diffractive Scattering
• Statistics of Transmission Eigenvalues in Two-Dimensional Quantum Cavities: Ballistic versus Stochastic Scattering