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Stability of wave-packet dynamics under perturbations.
Jens Bolte1, Tobias Schwaibold
1Abteilung Theoretische Physik, Universität Ulm, Albert-Einstein-Allee 11, D-89069 Ulm, Germany. jens.bolte@uni-ulm.de
Summary
We present a nonperturbative method to analyze wave-packet stability under Hamiltonian perturbations. Fidelity decay is linked to wave packet dispersion and classical trajectory separation, often showing exponential or doubly exponential decay.
Area of Science:
- Quantum dynamics
- Semiclassical approximations
- Chaos theory
Background:
- Investigating the stability of quantum systems is crucial for understanding their behavior under external influences.
- Perturbations to the Hamiltonian can lead to complex dynamics and potential instabilities.
Purpose of the Study:
- To develop a nonperturbative method for assessing the stability of wave-packet dynamics.
- To identify and quantify the factors contributing to quantum fidelity decay under Hamiltonian perturbations.
Main Methods:
- Utilizing semiclassical approximations for a nonperturbative analysis.
- Decomposing quantum fidelity into contributions from wave packet dispersion and classical trajectory separation.
- Estimating fidelity decay using classical Lyapunov exponents.
Main Results:
- Identified two key contributions to quantum fidelity decay.
- Demonstrated that fidelity decay is typically at least exponential.
- Showed that doubly exponential decay occurs for specific systems like inverted harmonic oscillators.
Conclusions:
- The developed method provides insights into the stability of quantum dynamics.
- Classical Lyapunov exponents are effective in estimating fidelity decay rates.
- The nature of fidelity decay (exponential vs. doubly exponential) depends on the system's properties.