Real-time correlators in chaotic quantum many-body systems

Understand

We study real-time local correlators $\langle\mathcal{O}(\mathbf{x},t)\mathcal{O}(0,0)\rangle$ in chaotic quantum many-body systems.

• These correlators show universal structure at late times, determined by the dominant operator-space Feynman trajectories for the evolving operator $\mathcal{O}(\mathbf{x},t)$.
• The relevant trajectories involve the operator contracting to a point at both the initial and final time and so are structurally different from those dominating the out-of-time-order correlator.
• In the absence of conservation laws, correlations decay exponentially: $\langle\mathcal{O}(\mathbf{x},t)\mathcal{O}(0,0)\rangle\sim\exp(-s_\mathrm{eq} r(\mathbf{v}) t)$, where $\mathbf{v}= \mathbf{x}/ t$ defines a spacetime ray, and $r(\mathbf{v})$ is an associated decay rate.