Dynamical quantum ergodicity from energy level statistics

Understand

Ergodic theory provides a rigorous mathematical description of chaos in classical dynamical systems, including a formal definition of the ergodic hierarchy.

• How ergodic dynamics is reflected in the energy levels and eigenstates of a quantum system is the central question of quantum chaos, but a rigorous quantum notion of ergodicity remains elusive.
• Closely related to the classical ergodic hierarchy is a less-known notion of cyclic approximate periodic transformations [see, e.g., I.
• Cornfield, S.