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arXiv · 1804.10543

Quantum chaos and entanglement in ergodic and non-ergodic systems

Angelo Piga·Maciej Lewenstein·James Q. Quach
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Abstract

We study entanglement entropy (EE) as a signature of quantum chaos in ergodic and non-ergodic systems. In particular we look at the quantum kicked top and kicked rotor as multi-qubit systems, and investigate the single qubit EE which characterizes bipartite entanglement of this qubit with the rest of the system. We study the correspondence of the Kolmogorov-Sinai entropy of the classical kicked systems with the EE of their quantum counterparts. We find that EE is a signature of global chaos in ergodic systems, and local chaos in non-ergodic systems. In particular, we show that EE can be maximised even when systems are highly non-ergodic, when the corresponding classical system is locally chaotic. In contrast, we find evidence that the quantum analogue of Kolmogorov-Arnol'd-Noser (KAM) tori are tori of low entanglement entropy. We conjecture that entanglement should play an important role in any quantum KAM theory.

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Angelo Piga, Maciej Lewenstein, James Q. Quach. 2018-04-27. Quantum chaos and entanglement in ergodic and non-ergodic systems. https://doi.org/10.1103/physreve.99.032213

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