Unbounded fluctuations in transport through an integrable cavity

TL;DR

This paper introduces a semiclassical approach to analyze conductance in an integrable cavity, revealing unbounded fluctuations and unique correlation properties distinct from chaotic systems.

Contribution

It develops a novel semiclassical scheme expressing transmission as a sum over trajectory families using continued fractions, highlighting differences from chaotic cavity conductance.

Findings

Conductance fluctuations grow with incoming energy.

Correlation function shows a singularity at zero.

Fluctuation behavior differs from chaotic cavities.

Abstract

We derive a semiclassical scheme for the conductance through a rectangular cavity. The transmission amplitudes are expressed as a sum over families of trajectories rather than a sum over isolated trajectories. The contributing families are obtained from the evaluation of a finite number of continued fractions. We find that, contrary to the chaotic case, the conductance fluctuations increase with the incoming energy and the correlation function exhibits a singularity at the origin.