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Relativistic quantum level-spacing statistics in chaotic graphene billiards
Liang Huang1, Ying-Cheng Lai, Celso Grebogi
1School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, Arizona 85287, USA.
Quantum dynamics in graphene show Gaussian orthogonal ensemble (GOE) level statistics, which change to Gaussian unitary ensemble (GUE) under weak magnetic fields. Strong fields restore GOE statistics due to Landau levels.
Area of Science:
- Quantum nonlinear dynamics
- Condensed matter physics
- Quantum chaos
Background:
- Understanding energy-level statistics in relativistic quantum systems is a key challenge.
- Graphene's unique electronic properties, governed by the Dirac equation, offer a platform for studying quantum chaos.
- Relativistic quantum systems present complex dynamics and statistical behaviors.
Purpose of the Study:
- To investigate the energy-level statistics in chaotic graphene confinements.
- To explore the influence of magnetic fields on these statistics.
- To connect experimental observations with random matrix theory predictions.
Main Methods:
- Utilizing chaotic graphene structures with low-energy Dirac fermions.
- Analyzing electronic motion governed by the Dirac equation.
- Applying random matrix theory, specifically Gaussian orthogonal ensemble (GOE) and Gaussian unitary ensemble (GUE).
Main Results:
- Level-spacing statistics in graphene confinements follow GOE predictions.
- Weak magnetic fields induce a transition to GUE statistics.
- Strong magnetic fields restore GOE statistics due to the formation of Landau levels.
Conclusions:
- Graphene systems exhibit quantum chaotic behavior consistent with random matrix theory.
- Magnetic fields provide a tunable parameter to control quantum statistical properties in graphene.
- The findings offer insights into quantum nonlinear dynamics in relativistic systems.
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