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Published on: December 10, 2008
Criticality in the quantum kicked rotor with a smooth potential
1Department of Physics, Indian Institute of Technology, Kharagpur, India.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 15, 2008
Summary
We found a quantum phase transition in the quantum kicked rotor model, showing characteristics of critical behavior and indicating a shift from localization to delocalization. This transition occurs at a specific kicking strength, revealing new physics in chaotic quantum systems.
Area of Science:
- Quantum chaos
- Condensed matter physics
- Statistical mechanics
Background:
- The quantum kicked rotor is a paradigmatic model for studying quantum chaos.
- Anderson-type transitions are fundamental phenomena in disordered systems, marking a transition from localized to delocalized states.
- Understanding transitions in quantum chaotic systems is crucial for fundamental physics.
Purpose of the Study:
- To investigate the possibility of an Anderson-type transition in the quantum kicked rotor with a smooth potential.
- To identify critical behaviors and transitions in the quantum kicked rotor model.
- To explore symmetry-breaking effects on transitions within the chaotic regime.
Main Methods:
- Numerical simulations of the quantum kicked rotor model.
- Analysis of wave function properties, including multifractality.
- Examination of energy level statistics for scale-invariance.
Main Results:
- Observed critical behavior characterized by multifractal eigenfunctions and scale-invariant level statistics at a critical kicking strength.
- Identified a localization to delocalization transition, analogous to Anderson transitions.
- Revealed additional transitions within the strongly chaotic regime driven by symmetry breaking (time reversal, parity).
Conclusions:
- The quantum kicked rotor exhibits an Anderson-type localization-delocalization transition.
- Symmetry breaking can drive novel transitions in quantum chaotic systems.
- These findings offer insights into quantum phase transitions and chaos in quantum systems.
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