https://doi.org/10.1140/epjc/s10052-022-10035-3
Regular Article - Theoretical Physics
Towards the web of quantum chaos diagnostics
1
Indian Institute of Technology, 382355, Gandhinagar, Gujarat, India
2
Institute for Quantum Information and Matter, California Institute of Technology, 1200 E California Blvd, 91125, Pasadena, CA, USA
3
Department of Mathematics and Applied Mathematics, University of Cape Town, Private Bag, 7701, Rondebosch, South Africa
4
Center for Nonlinear Studies, Los Alamos National Laboratory, 87544, Los Alamos, NM, USA
5
Theoretical Division, Los Alamos National Laboratory, 87544, Los Alamos, NM, USA
Received:
24
August
2021
Accepted:
14
January
2022
Published online:
29
January
2022
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.
© The Author(s) 2022
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