Out-of-time-ordered correlators of mean-field bosons via Bogoliubov theory

• URL: http://arxiv.org/abs/2312.01736v1
• Date: Mon, 4 Dec 2023 09:01:35 GMT
• Title: Out-of-time-ordered correlators of mean-field bosons via Bogoliubov theory
• Authors: Marius Lemm, Simone Rademacher
• Abstract summary: We show that the limit of the OTOC $langle [A(t),B]2rangle$ is explicitly given by a suitable symplectic Bogoliubov dynamics. Our result spotlights a new problem in nonlinear dispersive PDE with implications for quantum many-body chaos.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $\langle [A(t),B]^2\rangle$ can be connected to classical symplectic dynamics. We rigorously prove a variant of this correspondence principle for mean-field bosons. We show that the $N\to\infty$ limit of the OTOC $\langle [A(t),B]^2\rangle$ is explicitly given by a suitable symplectic Bogoliubov dynamics. The proof uses Bogoliubov theory and extends to higher-order correlators of observables at different times. For these, it yields an out-of-time-ordered analog of the Wick rule. Our result spotlights a new problem in nonlinear dispersive PDE with implications for quantum many-body chaos.

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