Semiclassical Theory of Many-Body Quantum Chaos and its Bound

Thomas Scaffidi, Ehud Altman

Published 2017-11-13Version 1

We introduce a direct quantum-classical correspondence for the chaotic dynamics of quantum many-body systems. The bound on chaos is understood as a "chaotic mobility edge" in the classical Lyapunov spectrum, separating the lower part of the spectrum for which a classical chaos picture applies from the higher part of the spectrum for which quantum interference effects destroy classical chaos. The dominant chaotic mode in bound-saturating systems is exactly at the "mobility edge" and therefore inherits a universal critical behavior. We provide an explicit example by introducing a classical version of the Sachdev-Ye-Kitaev (SYK) model for which chaos can be understood as arising from diverging geodesics on a high-dimensional manifold with a random metric.