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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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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Complexity measures in QFT and constrained geometric actions

    hep-th 2019-08 reject novelty 7.0 of 10

    The authors claim to rule out inhomogeneous complexity costs such as F_kappa and F_sigma^2 and to single out F_⟨H^2⟩ as the canonical complexity measure, but the no-go proof is incomplete.

  2. Towards the Web of Quantum Chaos Diagnostics

    hep-th 2019-09 conditional novelty 6.0 of 10

    Haar-averaged higher-point out-of-time-order correlators equal multi-fold Loschmidt echoes, and complexity is conjectured to satisfy C^2 ~ -log LE.

  3. 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.

  4. Dynamics of monitored SSH Model in Krylov Space: From Complexity to Quantum Fisher Information

    quant-ph 2025-02 conditional novelty 5.0 of 10

    Time-averaged quantum Fisher information in Krylov space changes slope at the PT transition (gamma=1) and saturates near the entanglement transition (gamma=2) in the monitored SSH model, suggesting it as a probe of both.

  5. Reflections on Virasoro circuit complexity and Berry phase

    hep-th 2019-08 reject novelty 3.0 of 10

    A claimed identification of Virasoro circuit complexity with the Berry connection fails a basic consistency check for pure rotations.

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