Fidelity amplitude of the scattering matrix in microwave cavities

TL;DR

This paper introduces the concept of scattering fidelity in microwave cavities, demonstrating its equivalence to the fidelity amplitude in chaotic systems through experiments that align with random matrix theory predictions.

Contribution

It defines scattering fidelity as a parametric cross-correlation of S-matrix elements and validates it experimentally against theoretical models for chaotic systems.

Findings

Scattering fidelity matches the fidelity amplitude in chaotic systems.

Experimental results agree with random matrix theory predictions.

Perturbation strength can be independently determined from level dynamics.

Abstract

The concept of fidelity decay is discussed from the point of view of the scattering matrix, and the scattering fidelity is introduced as the parametric cross-correlation of a given S-matrix element, taken in the time domain, normalized by the corresponding autocorrelation function. We show that for chaotic systems, this quantity represents the usual fidelity amplitude, if appropriate ensemble and/or energy averages are taken. We present a microwave experiment where the scattering fidelity is measured for an ensemble of chaotic systems. The results are in excellent agreement with random matrix theory for the standard fidelity amplitude. The only parameter, namely the perturbation strength could be determined independently from level dynamics of the system, thus providing a parameter free agreement between theory and experiment.