Experimental progress in atomic, molecular, and optical platforms in the last decade has
stimulated strong and broad interest in the quantum coherent dynamics of many long-range …

We review the effects of excited-state quantum phase transitions (ESQPTs) in interacting
many-body systems with finite numbers of collective degrees of freedom. We classify typical …

A bstract In semi-classical systems, the exponential growth of the out-of-time-order correlator
(OTOC) is believed to be the hallmark of quantum chaos. However, on several occasions, it …

Focusing on semiclassical systems, we show that the parametrically long exponential
growth of out-of-time order correlators (OTOCs), also known as scrambling, does not …

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 …

We show that out-of-time-order correlators (OTOCs) constitute a probe for local-operator
entanglement (LOE). There is strong evidence that a volumetric growth of LOE is a faithful …

Quantum scrambling describes the spreading of information into many degrees of freedom
in quantum systems, such that the information is no longer accessible locally but becomes …

A bstract We provide a detailed examination of a thermal out-of-time-order correlator (OTOC)
growing exponentially in time in systems without chaos. The system is a one-dimensional …

In quantum chaotic systems, the spectral form factor (SFF), defined as the Fourier transform
of two-level spectral correlation function, is known to follow random matrix theory (RMT) …

It is widely recognized that entanglement generation and dynamical chaos are intimately
related in semiclassical models via the process of decoherence. In this paper, we propose a …