Towards the Web of Quantum Chaos Diagnostics
arXiv:1909.01894 · doi:10.1140/epjc/s10052-022-10035-3
Abstract
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.
22 pages, 14 figures, 1 appendix. In this version the presentation has been improved, a few arguments have been strengthened, and three figures have been added
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