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Updated: Jun 14, 2026
06:42
Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
Quantum corrections to fidelity decay in chaotic systems
Boris Gutkin1, Daniel Waltner, Martha Gutiérrez
1Fachbereich Physik, Universität Duisburg-Essen, Lotharstrasse 1, D-47048 Duisburg, Germany.
Summary
We derived semiclassical expressions for quantum fidelity decay in chaotic systems. Our findings align with random matrix theory and reveal quantum corrections suppressed in certain regimes.
Area of Science:
- Quantum chaos
- Statistical mechanics
- Quantum dynamics
Background:
- Understanding quantum fidelity decay is crucial for characterizing quantum chaotic systems.
- Existing theories often rely on random matrix theory (RMT) or specific approximations.
Purpose of the Study:
- To derive semiclassical expressions for quantum fidelity amplitude and fidelity (Loschmidt echo) decay in classically chaotic systems.
- To unify the treatment of fidelity across different dynamical regimes (Fermi-golden rule and Lyapunov).
- To investigate quantum corrections and Ehrenfest-time effects on fidelity.
Main Methods:
- Utilizing correlations between classical orbits to develop semiclassical expressions.
- Comparing semiclassical results with random matrix theory (RMT) and supersymmetry predictions.
- Employing trajectory-based methods to establish relations with cross-form factors.
- Computing Ehrenfest-time effects beyond RMT.
Main Results:
- Semiclassical expressions for fidelity amplitude and fidelity decay were derived.
- Results agree with RMT and supersymmetry in the Fermi-golden rule regime.
- Quantum corrections arise from static random perturbations and are suppressed for time-varying ones.
- A relation between fidelity amplitude and cross-form factor was established.
- Ehrenfest-time effects on fidelity amplitude were computed.
- A unified treatment showed quantum corrections are suppressed in the Lyapunov regime.
Conclusions:
- The semiclassical approach provides a unified framework for studying quantum fidelity decay.
- Quantum corrections exhibit distinct behaviors depending on the dynamical regime and perturbation type.
- The study offers new insights into the interplay between classical dynamics and quantum fidelity in chaotic systems.
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