Failure of random matrix theory to correctly describe quantum dynamics

Consider a classically chaotic system that is described by a Hamiltonian [formula presented] At [formula presented] the Hamiltonian undergoes a sudden change [formula presented] We consider the quantum-mechanical spreading of the evolving energy distribution, and argue that it cannot be analyzed using a conventional random-matrix theory (RMT) approach. Conventional RMT can be trusted only to the extent that it gives trivial results that are implied by first-order perturbation theory. Nonperturbative effects are sensitive to the underlying classical dynamics, and therefore the [formula presented] behavior for effective RMT models is strikingly different from the correct semiclassical limit.