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Related Experiment Video

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Fabrication and Characterization of Superconducting Resonators

Fabrication and Characterization of Superconducting Resonators

Published on: May 21, 2016

Missing levels in acoustic resonators.

T N Nogueira¹, J C Sartorelli, M P Pato

¹Instituto de Física, Universidade de São Paulo, Caixa Postal 66318, 05315-970 São Paulo, SP, Brazil.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|December 31, 2008

Summary

This summary is machine-generated.

Deviations in chaotic acoustic resonators are explained by missing energy levels. A single parameter, the fraction of remaining levels, accurately fits experimental data for spectral rigidity and nearest-neighbor distributions.

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Area of Science:

Physics
Acoustics
Quantum Chaos

Background:

Wigner-Dyson random matrix theory (RMT) is a standard model for spectral statistics in chaotic systems.
Experimental data from chaotic acoustic resonators often show deviations from RMT predictions.
Understanding these deviations is crucial for refining theoretical models.

Purpose of the Study:

To explain the observed deviations in experimental statistics of chaotic acoustic resonators from Wigner-Dyson RMT predictions.
To validate a recent model of random missing levels in spectral analysis.
To quantify the fraction of undetected eigenfrequencies in various resonator shapes.

Main Methods:

Comparison of experimental spectral statistics (spectral rigidity and nearest-neighbor distributions) with Wigner-Dyson RMT predictions.
Application of a model accounting for random missing levels.
Adjustment of a single parameter representing the fraction of remaining levels to fit experimental data.

Main Results:

The model of random missing levels successfully explains the deviations observed in six chaotic acoustic resonators.
Larger deviations were noted in spectral rigidity (SRs), while nearest-neighbor distributions (NNDs) remained close to the Wigner surmise.
A good fit to experimental NNDs and SRs was achieved by adjusting the fraction of remaining levels.
Specific fractions of undetected eigenfrequencies were determined for different resonator shapes: 7% (two Sinai stadiums), 4% (one Sinai stadium without planar symmetry), 7% (two triangles), and 2% (three-leaf clover).

Conclusions:

The model of random missing levels provides a robust explanation for experimental deviations in chaotic acoustic resonator statistics.
The fraction of missing levels is a key parameter that reconciles experimental data with theoretical predictions.
This approach offers a quantitative method to assess the completeness of detected eigenfrequencies in complex systems.