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Entanglement in coupled kicked tops with chaotic dynamics
Tabea Herrmann1, Maximilian F I Kieler1, Felix Fritzsch1
1Technische Universität Dresden, Institut für Theoretische Physik and Center for Dynamics, 01062 Dresden, Germany.
Physical Review. E
|March 15, 2020
Summary
We studied quantum entanglement in chaotic systems. A universal parameter governs the transition to random matrix behavior, showing consistent scaling for entanglement statistics across different subsystem sizes.
Area of Science:
- Quantum chaos
- Quantum information theory
- Statistical mechanics
Background:
- Understanding quantum entanglement in complex systems is crucial for quantum information science.
- Classically chaotic systems offer a unique platform to study quantum entanglement properties.
- The transition to random matrix theory (RMT) behavior signifies complex quantum dynamics.
Purpose of the Study:
- To investigate the entanglement of eigenstates in two coupled, classically chaotic kicked tops.
- To analyze the influence of interaction strength on quantum entanglement.
- To identify universal scaling laws governing the transition from noninteracting to RMT behavior.
Main Methods:
- Studied the entanglement of eigenstates in coupled kicked tops as a function of interaction strength.
- Employed random matrix transition ensembles to analyze the transition parameter.
- Investigated level spacing statistics, Schmidt eigenvalues, and entanglement entropies.
Main Results:
- A universal scaling parameter governs the transition to RMT behavior.
- Universality confirmed for level spacing statistics, Schmidt eigenvalues, and entanglement entropies.
- Perturbative descriptions show good agreement with numerical results for entanglement entropies.
Conclusions:
- Quantum entanglement in coupled chaotic systems exhibits universal scaling laws.
- The transition to RMT behavior is predictable and dependent on subsystem sizes and coupling strength.
- Perturbative methods provide accurate descriptions of entanglement properties, even for large couplings.
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