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Stability of quantum motion in regular systems: a uniform semiclassical approach
Wen-ge Wang1, G Casati, Baowen Li
1Department of Physics and Centre for Computational Science and Engineering, National University of Singapore, 117542, Republic of Singapore.
Summary
We analyzed quantum motion stability in perturbed classical systems. Our findings reveal complex fidelity decay, transitioning from Gaussian to power-law behavior, confirmed by numerical simulations.
Area of Science:
- Quantum mechanics
- Classical dynamics
- Chaos theory
Background:
- Understanding the stability of quantum systems is crucial for quantum computing and quantum information.
- Classically regular systems can exhibit complex quantum behavior under perturbation.
Purpose of the Study:
- To investigate the stability of quantum motion in classically regular systems subjected to small perturbations.
- To derive and analyze the fidelity decay in such systems using a semiclassical approach.
Main Methods:
- Development of a uniform semiclassical theory.
- Derivation of fidelity decay functions.
- Numerical simulations to validate theoretical predictions.
Main Results:
- Fidelity decay exhibits complex behavior, including Gaussian and power-law (t^-alpha, 1 <= alpha <= 2) regimes.
- Semiclassical estimates provide time scales for transitions between decay regions.
- Numerical results confirm the theoretical predictions for fidelity decay.
Conclusions:
- The study provides a theoretical framework for understanding quantum system stability under perturbation.
- The derived fidelity decay provides insights into the quantum-classical correspondence for regular systems.
- The findings have implications for the decoherence and error dynamics in quantum systems.
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