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Fluctuations and transients in quantum-resonant evolution.
Itzhack Dana1, Dmitry L Dorofeev
1Minerva Center and Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 13, 2006
Summary
The quantum-resonant evolution of mean kinetic energy (MKE) in kicked particles shows linear growth with fluctuations. These fluctuations and transient corrections depend on number theory and can vanish under specific conditions.
Area of Science:
- Quantum dynamics
- Statistical physics
- Mathematical physics
Background:
- Understanding the long-term behavior of quantum systems is crucial.
- Quantum resonance phenomena can lead to complex energy evolutions.
- Periodic potentials are fundamental in various quantum models.
Purpose of the Study:
- To investigate the quantum-resonant evolution of mean kinetic energy (MKE) for kicked particles.
- To analyze MKE behavior across different time scales and kicking potentials.
- To identify the origins and characteristics of MKE fluctuations and transients.
Main Methods:
- Detailed analysis of quantum-resonant evolution.
- Study of wave-packet dynamics under periodic potentials.
- Examination of MKE on various time scales.
Main Results:
- Asymptotic MKE typically exhibits linear growth with bounded, number-theoretically derived fluctuations.
- MKE often comprises asymptotic behavior plus transient logarithmic corrections.
- Fluctuations and transients can be significant but may vanish under certain conditions.
- Incoherent plane wave mixtures lack asymptotic fluctuations but show transients.
Conclusions:
- The MKE of kicked particles displays predictable asymptotic behavior with number-theoretic fluctuations.
- Transient effects play a role in MKE evolution, varying with wave packet properties.
- Understanding these dynamics is key for quantum system analysis.
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