Signatures of Quantum Chaos in Classically Non-Chaotic Systems

One of the original goals in the field of quantum chaos was to establish a correspondence between the dynamics of chaotic classical systems and their quantum counterparts. The general issue is that quantum-mechanical interference washes out classical chaos after a very short (logarithmic) time, and the correspondence breaks down. Recently, out-of-time-ordered correlator, a universal tool to study quantum chaos, has received a lot of attention due to its versatility and natural interpretation. We use this diagnostic to show that a new kind of drastic disagreement can occur between quantum and classical counterparts of the same model. Remarkably, quantum mechanics appears capable of playing the opposite to its usual role. In particular, it brings chaos to a family of classically non-chaotic systems, where on the quantum side, we demonstrate the Lyapunov-like exponential growth of OTOC.