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Chaos and Complexity in Quantum Mechanics

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arxiv 1905.13534 v4 pith:GCA74DDV submitted 2019-05-31 hep-th nlin.CDquant-ph

Tibra Ali , Arpan Bhattacharyya , S. Shajidul Haque , Eugene H. Kim , Nathan Moynihan , Jeff Murugan This is my paper · ORCID
classification hep-thnlin.CDquant-ph
keywords timecomplexitychaoschaoticquantumregularscalebehaviour
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We propose a new diagnostic for quantum chaos. We show that time evolution of complexity for a particular type of target state can provide equivalent information about the classical Lyapunov exponent and scrambling time as out-of-time-order correlators. Moreover, for systems that can be switched from a regular to unstable (chaotic) regime by a tuning of the coupling constant of the interaction Hamiltonian, we find that the complexity defines a new time scale. We interpret this time scale as recording when the system makes the transition from regular to chaotic behaviour.

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  1. Probing the self-coherence of primordial quantum fluctuations with complexity

    hep-th 2025-02 conditional novelty 5.0 of 10

    Complexity of formation, unlike complexity of purification, shows distinct and timescale-matching signatures of both decoherence and recoherence in a Gaussian two-field de Sitter model.

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