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Published on: October 5, 2018
Anderson transition in a three-dimensional kicked rotor
Jiao Wang1, Antonio M García-García
1Temasek Laboratories, National University of Singapore, 117542 Singapore.
Summary
We studied Anderson localization in a 3D kicked rotor, finding a mobility edge. For strong kicking, states delocalize, unlike predictions for non-random potentials which can enhance localization.
Area of Science:
- Quantum chaos
- Condensed matter physics
- Anderson localization
Background:
- Anderson localization describes the suppression of quantum diffusion in disordered systems.
- The kicked rotor model is a paradigm for studying quantum chaos and localization phenomena.
Purpose of the Study:
- Investigate Anderson localization in a three-dimensional (3D) kicked rotor system.
- Identify the conditions for dynamical localization and delocalization.
- Compare deterministic and random kicked rotor models.
Main Methods:
- Finite-size scaling analysis to identify the mobility edge.
- Numerical simulations of quantum diffusion and level statistics.
- Mapping the kicked rotor to a 3D Anderson model.
Main Results:
- A mobility edge was identified at a critical kicking strength (k(c)).
- Above k(c), eigenstates delocalize, exhibiting Wigner-Dyson statistics.
- Anomalous quantum diffusion (
- Deterministic and random kicked rotors show similar behavior, but certain irrational periods enhance localization.
Conclusions:
- The 3D kicked rotor exhibits a transition from localized to delocalized states.
- The system's behavior aligns with the 3D Anderson model and one-parameter scaling theory.
- Deterministic potentials can exhibit stronger localization effects than random potentials under specific conditions.
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