Out-of-time-ordered correlators of mean-field bosons via Bogoliubov theory
arXiv:2312.01736 · doi:10.22331/q-2025-01-13-1587
Abstract
Quantum many-body chaos concerns the scrambling of quantum information among large numbers of degrees of freedom. It rests on the prediction that out-of-time-ordered correlators (OTOCs) of the form can be connected to classical symplectic dynamics. We rigorously prove a variant of this correspondence principle for mean-field bosons. We show that the limit of the OTOC is explicitly given by a suitable symplectic Bogoliubov dynamics. In practical terms, we describe the dynamical build-up of many-body entanglement between a particle and the whole system by an explicit nonlinear PDE on . For higher-order correlators, we obtain an out-of-time-ordered analog of the Wick rule. The proof uses Bogoliubov theory. Our finding spotlights a new problem in nonlinear dispersive PDE with implications for quantum many-body chaos.
arXiv comment41 pages; revised version to appear in Quantum
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