Semiclassical roots of universality in many-body quantum chaos

Quantum chaos of many-body (MB) systems has been swiftly developing into a vibrant research area at the interface between various disciplines, ranging from statistical physics to condensed matter to quantum information and to cosmology. In quantum systems with a classical limit, advanced semiclassical methods provide the crucial link between classically chaotic dynamics and corresponding universal features at the quantum level. Recently, single-particle (SP) techniques dealing with ergodic wave interference in the usual semiclassical limit have begun to be transformed into the field theoretical domain of N-particle systems in the analogous semiclassical limit , thereby accounting for genuine MB quantum interference. This semiclassical MB theory provides a unified framework for understanding random-matrix correlations of both SP and MB quantum chaotic systems. Certain braided bundles of classical orbits, and of mean field modes, govern interference, respectively, and provide the key to the foundation of universality. Case studies presented include an MB version of Gutzwiller’s trace formula for the spectral density and out-of-time-order correlators along with brief remarks on where further progress may be forthcoming