Quantum chaos and entanglement in ergodic and non-ergodic systems
arXiv:1804.10543 · doi:10.1103/PhysRevE.99.032213
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.
arXiv comment13 pages, 7 figures
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