The Onset of Quantum Chaos in Disordered Systems

We study the Lyapunov exponent in disordered quantum field theories. Generically the Lyapunov exponent can only be computed in isolated CFTs, and little is known about the way in which chaos grows as we deform the theory away from weak coupling. In this paper we describe families of theories in which the disorder coupling is an exactly marginal deformation, allowing us to follow the Lyapunov exponent from weak to strong coupling. We find surprising behaviors in some cases, including a discontinuous transition into chaos. We also describe a new method allowing for computations in nontrivial CFTs deformed by disorder at leading order in 1/N.