Sensing Small Changes in a Wave Chaotic Scattering System

TL;DR

This paper develops classical analogs of quantum fidelity concepts to detect small perturbations in wave chaotic systems, using time-reversal techniques and scattering fidelity measures, with experimental validation in acoustic cavities.

Contribution

It introduces novel sensing techniques based on time-reversal and scattering fidelity for detecting small perturbations in wave chaotic systems, bridging quantum concepts with classical wave sensing.

Findings

Effective detection of boundary and medium perturbations in acoustic cavities.

Mitigation of dissipation effects through signal processing.

Validation of techniques for real-world sensing applications.

Abstract

Classical analogs of the quantum mechanical concepts of the Loschmidt Echo and quantum fidelity are developed with the goal of detecting small perturbations in a closed wave chaotic region. Sensing techniques that employ a one-recording-channel time-reversal-mirror, which in turn relies on time reversal invariance and spatial reciprocity of the classical wave equation, are introduced. In analogy with quantum fidelity, we employ Scattering Fidelity techniques which work by comparing response signals of the scattering region, by means of cross correlation and mutual information of signals. The performance of the sensing techniques is compared for various perturbations induced experimentally in an acoustic resonant cavity. The acoustic signals are parametrically processed to mitigate the effect of dissipation and to vary the spatial diversity of the sensing schemes. In addition to static boundary condition perturbations at specified locations, perturbations to the medium of wave propagation are shown to be detectable, opening up various real world sensing applications in which a false negative cannot be tolerated.