Abstract The Sachdev–Ye–Kitaev model and two-dimensional dilaton gravity have recently
been attracting increasing attention of the high-energy and condensed-matter physics …

This tutorial article introduces the physics of quantum information scrambling in quantum
many-body systems. The goals are to understand how to precisely quantify the spreading of …

Quantum Chaos has originally emerged as the field which studies how the properties of
classical chaotic systems arise in their quantum counterparts. The growing interest in …

We demonstrate analytically and verify numerically that the out-of-time order correlator is
given by the thermal average of Loschmidt echo signals. This provides a direct link between …

Many-body chaos has emerged as a powerful framework for understanding thermalization in
strongly interacting quantum systems. While recent analytic advances have sharpened our …

The harmonic oscillator is the paragon of physical models; conceptually and computationally
simple, yet rich enough to teach us about physics on scales that span classical mechanics to …

Out-of-time-order correlators are widely used as an indicator of quantum chaos but give
false-positive quantum Lyapunov exponents for integrable systems with isolated saddle …

A bstract A simple probe of chaos and operator growth in many-body quantum systems is
the out of time ordered four point function. In a large class of local systems, the effects of …

We present a systematic construction of probes into the dynamics of isospectral ensembles
of Hamiltonians by the notion of Isospectral twirling, expanding the scopes and methods of …

A bstract We study three prominent diagnostics of chaos and scrambling in the context of two-
dimensional conformal field theory: the spectral form factor, out-of-time-ordered correlators …