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

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 $⟨[A(t),B{]}^2⟩$ 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 $⟨[A(t),B{]}^2⟩$ 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 $L^2({\mathbb{R}}^3)\oplus L^2({\mathbb{R}}^3)$. 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.

41 pages; revised version to appear in Quantum

References in corpus (20)

• Dynamics of Loschmidt echoes and fidelity decay
• Theory of universal incoherent metallic transport
• Lyapunov Exponent and Out-of-Time-Ordered Correlator's Growth Rate in a Chaotic System
• Microscopic model of quantum butterfly effect: out-of-time-order correlators and traveling combustion waves
• On the Mean-Field Limit of Bosons with Coulomb Two-Body Interaction
• Probing quantum information propagation with out-of-time-ordered correlators
• Scrambling Dynamics and Out-of-Time Ordered Correlators in Quantum Many-Body Systems: a Tutorial
• Charge diffusion and the butterfly effect in striped holographic matter
• Out-of-time-order correlations and Floquet dynamical quantum phase transition
• Lieb-Robinson bound and almost-linear light-cone in interacting boson systems
• Quantum Dynamics with Mean Field Interactions: a New Approach
• On Lieb-Robinson bounds for the Bose-Hubbard model
• Finite speed of quantum information in models of interacting bosons at finite density
• Effective light cone and digital quantum simulation of interacting bosons
• Large deviation estimates for weakly interacting bosons
• Optimal light cone for macroscopic particle transport in long-range systems: A quantum speed limit approach
• Diagnosing quantum chaos with out-of-time-ordered-correlator quasiprobability in the kicked-top model
• Weak Edgeworth expansion for the mean-field interacting Bose gas
• A note on dependent random variables in quantum dynamics
• On propagation of information in quantum many-body systems

Cited by in corpus (1)

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