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Related Experiment Video

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Algebraic fidelity decay for local perturbations.

R Höhmann1, U Kuhl, H-J Stöckmann

  • 1Fachbereich Physik, Philipps-Universität Marburg, Renthof 5, D-35032 Marburg, Germany.

Physical Review Letters
|June 4, 2008
PubMed
Summary

This study investigates fidelity decay in microwave billiards with random scatterers. Local perturbations from scatterer shifts cause an algebraic decay, matching experimental results.

Area of Science:

  • Quantum chaos
  • Wave scattering in complex systems

Background:

  • Fidelity decay in quantum systems is crucial for understanding their dynamics.
  • Microwave billiards with scatterers provide a platform to study wave phenomena.

Purpose of the Study:

  • To analyze fidelity decay in a rectangular microwave billiard with randomly distributed scatterers.
  • To investigate the effect of local perturbations, specifically scatterer position shifts, on wave function fidelity.

Main Methods:

  • Reflection measurements in a rectangular microwave billiard.
  • Perturbation analysis using scatterer position as the parameter.
  • Application of the random-plane-wave conjecture for theoretical modeling.

Main Results:

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  • An analytic expression for fidelity decay due to scatterer shifts was derived.
  • An algebraic 1/t decay for fidelity was predicted for long times.
  • Excellent agreement between experimental data and theoretical predictions was observed, including scaling behavior.
  • Conclusions:

    • Local perturbations from scatterer shifts lead to predictable fidelity decay.
    • The random-plane-wave conjecture accurately describes fidelity decay in this system.
    • Experimental validation confirms the theoretical model and its predictions.