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Hierarchical structures in the phase space and fractional kinetics: II. Immense delocalization in quantized systems
1Department of Physics, Technion, Haifa 32000, Israel.
Chaos (Woodbury, N.Y.)
|June 5, 2003
Summary
Quantum systems exhibit anomalous transport via Levy-type flights. Special parameter values dramatically increase localization length and delocalization in kicked rotor and Harper models.
Area of Science:
- Quantum chaos
- Anomalous transport phenomena
- Statistical physics
Background:
- Quantum kicked systems, such as the kicked rotor and kicked Harper model, display complex dynamics.
- Anomalous transport, characterized by Levy-type flights, deviates from standard diffusive behavior.
Purpose of the Study:
- To investigate anomalous transport in quantum kicked systems.
- To identify conditions leading to enhanced localization length and delocalization.
- To explore the relationship between system parameters and phase space topology.
Main Methods:
- Analysis of quantum kicked rotor and kicked Harper models.
- Numerical investigation of localization length.
- Examination of phase space topology in the classical limit.
Main Results:
- "Magic" parameter values (K(*) = 6.908 745 for kicked rotor, K(*) = 6.349 972 for kicked Harper model) were found to significantly increase localization length.
- Immense delocalization (order of 10^9) was observed in the kicked Harper model at its magic parameter value.
- The observed effects correlate with specific phase space topologies, including hierarchical self-similar structures.
Conclusions:
- Anomalous transport in quantum kicked systems can lead to significant delocalization and increased localization length.
- The identified "magic" parameter values are linked to unique classical phase space structures.
- The underlying principles are general and applicable to other quantum systems exhibiting similar dynamics.
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