Fidelity serves as a benchmark for the reliability in quantum information processes, and has
recently attracted much interest as a measure of the susceptibility of dynamics to …

During the last few years quantum graphs have become a paradigm of quantum chaos with
applications from spectral statistics to chaotic scattering and wavefunction statistics. In the …

The most general and versatile defining feature of quantum chaotic systems is that they
possess an energy spectrum with correlations universally described by random matrix …

The distinction between level clustering and level repulsion is one of the quantum
analogues of the classical distinction between globally regular and predominantly chaotic …

A bstract We introduce a framework for quantifying random matrix behavior of 2d CFTs and
AdS 3 quantum gravity. We present a 2d CFT trace formula, precisely analogous to the …

A key goal of quantum chaos is to establish a relationship between widely observed
universal spectral fluctuations of clean quantum systems and random matrix theory (RMT) …

Quantum chaotic systems are often defined via the assertion that their spectral statistics
coincides with, or is well approximated by, random matrix theory. In this paper we explain …

Out-of-time-order correlators (OTOCs) have been proposed as sensitive probes for chaos in
interacting quantum systems. They exhibit a characteristic classical exponential growth, but …

A bstract We conjecture a formula for the spectral form factor of a double-scaled matrix
integral in the limit of large time, large density of states, and fixed temperature. The formula …

We review various bounds concerning out-of-equilibrium dynamics in few-level and many-
body quantum systems. We primarily focus on closed quantum systems but will also mention …