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 …

Interpreting wave phenomena in terms of an underlying ray dynamics adds a new
dimension to the analysis of linear wave equations. Forming explicit connections between …

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 …

We sketch the semiclassical core of a proof of the so-called Bohigas-Giannoni-Schmit
conjecture: A dynamical system with full classical chaos has a quantum energy spectrum …

We argue semiclassically, on the basis of Gutzwiller's periodic-orbit theory, that full classical
chaos is paralleled by quantum energy spectra with universal spectral statistics, in …

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 …

A long period of linear growth in the spectral form factor provides a universal diagnostic of
quantum chaos at intermediate times. By contrast, the behavior of the spectral form factor in …

This volume is a collection of articles dedicated to quantum graphs, a newly emerging
interdisciplinary field related to various areas of mathematics and physics. The reader can …

We present an extensive numerical study of spectral statistics and eigenfunctions of
quantized triangular billiards. We compute two million consecutive eigenvalues for six …

One manifestation of quantum chaos is a random-matrix-like fine-grained energy spectrum.
Prior to the inverse level spacing time, random matrix theory predicts a “ramp” of increasing …