Quantum Chaos Without a Classical Correspondence

Classical chaos is a mathematically well-defined concept, but its precise meaning in the quantum realm remains elusive. Over the past decade, research on quantum chaos has advanced mainly along two complementary directions. The first seeks quantum analogues of classical Lyapunov instability through out-of-time-ordered correlators, particularly in many-body systems and quantum field theories in a large-N regime. The second characterizes quantum chaos through random-matrix universality—for example, in spectral statistics. This provides a more abstract and broadly applicable notion of quantum chaos that does not rely on a classical correspondence or on the existence of a small or large parameter. I will discuss a class of models exemplifying the second approach: dual-unitary systems and their perturbations. For these models, one can derive exact—and often rigorous—results for spectral statistics, operator growth, and other measures of dynamical complexity. They therefore provide a controlled setting in which to explore what quantum chaos means in the absence of a classical counterpart.