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Fractional dynamics in the Lévy quantum kicked rotor
1Instituto de Física, Facultad de Ingeniería Universidad de la República, C.C. 30, C.P. 11000, Montevideo, Uruguay. alejo@fing.edu.uy
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 31, 2008
Summary
Quantum systems with Lévy measurements exhibit sub-ballistic behavior. Researchers derived an analytical formula for diffusion exponent, linking it to fractional dynamics.
Area of Science:
- Quantum chaos
- Statistical mechanics
- Anomalous diffusion
Background:
- The quantum kicked rotor is a paradigmatic model for studying quantum chaos.
- Resonance conditions can lead to anomalous diffusion in quantum systems.
- Momentum measurements introduce non-trivial dynamics and waiting-time distributions.
Purpose of the Study:
- To investigate the behavior of the quantum kicked rotor under resonance conditions with Lévy waiting-time distributions for momentum measurements.
- To analytically determine the diffusion exponent and its dependence on Lévy distribution parameters.
- To establish a connection between the observed anomalous diffusion and fractional dynamics.
Main Methods:
- Numerical simulations of the quantum kicked rotor model.
- Application of Lévy waiting-time distributions to momentum measurements.
- Derivation of analytical expressions for the variance and diffusion exponent.
- Analysis of the system's dynamics in the context of fractional calculus.
Main Results:
- The quantum kicked rotor system exhibits sub-ballistic behavior under the specified conditions.
- An analytical expression for the power-law exponent of the variance was obtained.
- This exponent was found to be a function of the characteristic parameter of the Lévy distribution.
- A direct link between the anomalous diffusion and fractional dynamics was established.
Conclusions:
- Lévy waiting-time distributions in momentum measurements induce sub-ballistic anomalous diffusion in the resonant quantum kicked rotor.
- The derived analytical expression provides a quantitative understanding of the diffusion process.
- The connection to fractional dynamics offers a new perspective for analyzing complex quantum transport phenomena.
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