Bridging entanglement dynamics and chaos in semiclassical systems

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Paper Summary

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Quantum Entanglement: How Chaos Makes It Grow (Faster!)

This theoretical paper proposes a unifying framework linking quantum entanglement and classical chaos in many-particle systems. It finds that entanglement measures (entropy, Fisher information, square commutator) grow logarithmically/quadratically in regular systems but linearly/exponentially in chaotic ones, confirming previous conjectures. Numerical simulations of kicked top and Dicke models support these analytical predictions, though numerical precision limitations affect classical simulations in chaotic regimes over long times.

Possible Conflicts of Interest

None identified

Identified Weaknesses

Numerical Integration Limitations

The classical simulations, especially in chaotic regimes, suffer from a lack of symplecticity in numerical integration, leading to violations of phase-space volume conservation. While mitigated with multi-precision arithmetic, this restricts the validity of classical simulations to relatively short times.

Discrepancy with Asymptotic Lyapunov Exponents

The paper notes that the growth rates often deviate from the proper asymptotic Lyapunov exponents, particularly in mixed regular-chaotic phase spaces. This indicates a more complex relationship than a simple asymptotic correspondence, emphasizing the need to consider finite-time Lyapunov spectra.

Idealized Models

The study focuses on idealized collective spin models, which, while relevant for atomic and optical experiments, may not capture all complexities of real quantum many-body systems. Generalizability to all emergent semiclassical limits might need further validation.

Rating Explanation

This paper presents a strong theoretical framework with detailed analytical derivations and comprehensive numerical validation across different dynamical regimes. It addresses a fundamental question in quantum mechanics and provides clear quantitative predictions. The paper explicitly discusses and attempts to mitigate its numerical methodological limitations, demonstrating thoroughness, which leads to a high rating.

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