Fidelity amplitude of the scattering matrix in microwave cavities

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.

References in corpus (10)

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• Quantum Dynamical Echoes in the Spin 'Diffusion' in Mesoscopic Systems
• A random matrix formulation of fidelity decay
• Theory of quantum Loschmidt echoes
• Correlation functions of scattering matrix elements in microwave cavities with strong absorption
• Decoherence alias Loschmidt echo of the environment
• Fidelity recovery in chaotic systems and the Debye-Waller factor
• Recovery of the fidelity amplitude for the Gaussian ensembles
• Signatures of the correlation hole in total and partial cross sections
• Universality in quantum parametric correlations

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