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

Autor:	Lemm, Marius, Rademacher, Simone
Rok vydání:	2023
Předmět:	Mathematical Physics Quantum Physics
Druh dokumentu:	Working Paper
Popis:	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. Comment: 30 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2312.01736 Zobrazit plný text záznamu View this record from Arxiv