Towards the web of quantum chaos diagnostics

Journal Article · 28 January 2022 · European Physical Journal. C, Particles and Fields

DOI: https://doi.org/10.1140/epjc/s10052-022-10035-3 · OSTI ID:1855129

Yan, Bin  ^[1]; Bhattacharyya, Arpan ^[2]; Chemissany, Wissam  ^[3]; Haque, S. Shajidul ^[4]

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1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2. Indian Inst. of Technology (IIT), Gandhinagar (India)
3. California Institute of Technology (CalTech), Pasadena, CA (United States). Institute for Quantum Information and Matter
4. Univ. of Cape Town (South Africa)

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 investigated the relationship between a specific circuit complexity and LE by using the inverted oscillator model and made a conjecture about their relationship. These relationships signal a deeper connection between these three probes of quantum chaos.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: Board Of Research In Nuclear Sciences (BRNS), Department of Atomic Energy, India; Science and Engineering Research Board (India); USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division
• Grant/Contract Number: 89233218CNA000001
• OSTI ID: 1855129
• Report Number(s): LA-UR-19-28837
• Journal Information: European Physical Journal. C, Particles and Fields, Journal Name: European Physical Journal. C, Particles and Fields Journal Issue: 1 Vol. 82; ISSN 1434-6044
• Publisher: SpringerCopyright Statement
• Country of Publication: United States
• Language: English