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Decay of the Loschmidt echo for quantum states with sub-planck-scale structures
Ph Jacquod1, I Adagideli, C W J Beenakker
1Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, The Netherlands.
Physical Review Letters
|October 9, 2002
Summary
Quantum states with sub-Planck structures show accelerated decay in the Loschmidt Echo. This effect is driven by classical dynamics, not quantum interference, impacting quantum state sensitivity to perturbations.
Area of Science:
- Quantum mechanics
- Quantum chaos
- Statistical physics
Background:
- Quantum states can exhibit complex structures in phase space, including oscillations on sub-Planck scales.
- These structures arise from quantum interference phenomena.
Purpose of the Study:
- To investigate the impact of sub-Planck scale structures on the sensitivity of quantum states to external perturbations.
- To determine if quantum interference contributes to the decay of the Loschmidt Echo.
Main Methods:
- Analysis of quantum states with extended phase space distributions.
- Calculation of the Loschmidt Echo decay rate.
- Comparison of extended states with localized wave packets.
Main Results:
- Extended quantum states exhibit accelerated decay of the Loschmidt Echo compared to localized states.
- The observed acceleration in decay is fully explained by the classical Lyapunov exponent.
- Quantum interference effects on sub-Planck scales do not contribute to this accelerated decay.
Conclusions:
- Sub-Planck structures in quantum states do not enhance sensitivity to perturbations via quantum interference.
- The dynamics governing the decay of the Loschmidt Echo in these systems are predominantly classical.
- This finding clarifies the role of quantum interference versus classical chaos in quantum state stability.