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Towards the Web of Quantum Chaos Diagnostics

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arxiv 1909.01894 v2 pith:ELGPTMKZ submitted 2019-09-04 hep-th gr-qcquant-ph

Arpan Bhattacharyya , Wissam Chemissany , S. Shajidul Haque , Bin Yan This is my paper · ORCID
classification hep-thgr-qcquant-ph
keywords chaosquantumcomplexityconnectiondiagnosticsotocthreeapplications
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We study the connections between three quantities that can be used as diagnostics for quantum chaos, i.e., the out-of-time-order correlator (OTOC), Loschmidt echo (LE), and complexity. We generalize the connection between OTOC and LE for infinite dimensions and extend it for higher-order OTOCs and multi-fold LEs. Novel applications of this intrinsic relation are proposed. We also propose a relationship between a specific circuit complexity and LE by using the inverted oscillator model. These relationships signal a deeper connection between these three probes of quantum chaos.

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    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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