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Localization and fluctuations in quantum kicked rotors
I I Satija1, B Sundaram, J A Ketoja
1Department of Physics, George Mason University, Fairfax, Virginia 22030, USA. isatija@sitar.gmu.edu
Summary
We studied fluctuations in kicked quantum systems, finding a fractal nature. A new method links these fluctuations to the localization length, offering insights into quantum dynamics.
Area of Science:
- Quantum mechanics
- Statistical physics
Background:
- Dynamical localization in kicked quantum systems leads to fluctuations around exponential line shapes.
- Understanding these fluctuations is crucial for characterizing localization phenomena.
Purpose of the Study:
- To analyze fluctuations in one-dimensional kicked quantum systems.
- To establish a method for computing localization length from fluctuations.
- To compare fluctuation behavior in linear and quadratic rotor systems.
Main Methods:
- Exact renormalization scheme to analyze fractal properties of fluctuations.
- Calculation of localization length based on fluctuation characteristics.
Main Results:
- Identified fractal character of fluctuations in kicked quantum systems.
- Developed a method to compute localization length from fluctuations.
- Linear rotor: fluctuations are independent of kicking parameter and show self-similarity.
- Quadratic rotor: fluctuations depend on kicking strength, exhibiting resonances that cause deviations in localization length.
Conclusions:
- The fractal nature of fluctuations provides a computable link to localization length.
- Linear and quadratic rotors exhibit distinct fluctuation behaviors impacting localization characteristics.
- These findings offer a new perspective on quantum localization and its system-dependent features.