Universal S-matrix correlations for complex scattering of many-body wavepackets: theory, simulation and experiment

TL;DR

This paper investigates universal correlations in the scattering matrix for non-stationary many-body wavepacket scattering, combining theory, simulation, and microwave experiments to reveal signatures of chaotic dynamics.

Contribution

It introduces a semiclassical framework and numerical methods to analyze universal S-matrix correlations in non-stationary scattering, validated by experimental data.

Findings

Universal correlations persist in few-channel regimes.

Excellent agreement between theory, simulation, and experiment.

Chaotic signatures emerge in dynamical observables of wavepacket scattering.

Abstract

We present an in-depth study of the universal correlations of scattering-matrix entries required in the framework of non-stationary many-body scattering where the incoming states are localized wavepackets. Contrary to the stationary case the emergence of universal signatures of chaotic dynamics in dynamical observables manifests itself in the emergence of universal correlations of the scattering matrix at different energies. We use a semiclassical theory based on interfering paths, numerical wave function based simulations and numerical averaging over random-matrix ensembles to calculate such correlations and compare with experimental measurements in microwave graphs, finding excellent agreement. Our calculations show that the universality of the correlators survives the extreme limit of few open channels relevant for electron quantum optics, albeit at the price of dealing with large-cancellation effects requiring the computation of a large class of semiclassical diagrams.