Chaotic scattering through coupled cavities

TL;DR

This paper analyzes chaotic scattering in a coupled cavity system with one resonant and one chaotic cavity, revealing how conductance features depend on system parameters and symmetry classes using analytical and numerical methods.

Contribution

It provides an analytical framework for conductance in coupled cavities with chaotic dynamics, incorporating supersymmetry and random matrix theory, and explores symmetry effects on conductance oscillations.

Findings

Conductance is governed by the competition between mean and fluctuation parts.

Dephasing affects only the fluctuation part of conductance.

Resonant peaks transform into antiresonances with increasing level broadening ratio.

Abstract

We study the chaotic scattering through an Aharonov-Bohm ring containing two cavities. One of the cavities has well-separated resonant levels while the other is chaotic, and is treated by random matrix theory. The conductance through the ring is calculated analytically using the supersymmetry method and the quantum fluctuation effects are numerically investigated in detail. We find that the conductance is determined by the competition between the mean and fluctuation parts. The dephasing effect acts on the fluctuation part only. The Breit-Wigner resonant peak is changed to an antiresonance by increasing the ratio of the level broadening to the mean level spacing of the random cavity, and the asymmetric Fano form turns into a symmetric one. For the orthogonal and symplectic ensembles, the period of the Aharonov-Bohm oscillations is half of that for regular systems. The conductance distribution function becomes independent of the ensembles at the resonant point, which can be understood by the mode-locking mechanism. We also discuss the relation of our results to the random walk problem.