Quantum-Classical Correspondence and chaotic mobility edge for Fast Scramblers

We introduce a semiclassical version of the Sachdev-Ye-Kitaev model for which chaos can be understood as arising from diverging geodesics on a SO(N) manifold equipped with a random metric with locally negative curvature. The global Lyapunov exponent of the classical model is found to grow linearly with temperature, with a slope that can exceed the quantum bound. The bound on chaos is understood as a reversed ``chaotic mobility edge'' in the classical Lyapunov spectrum, separating the lower part of the spectrum for which a classical chaos picture is valid from the higher part of the spectrum for which quantum interference effects are strong enough to destroy chaos. The mobility edge corresponds to a curvature radius of the order of the de Broglie wavelength.