Fermi–Pasta–Ulam recurrences, normal modes and wave-packet revivals

A study of a chain of nonlinearly coupled oscillators which was performed in 1953 by Fermi, Pasta and Ulam showed that the energy which initially is deposited in a single mode does not dissipate irreversibly. Rather, after a recurrence time, the system returns to its initial state. Few experiments have been performed to prove the existence of these recurrences. We show that the underlying principle is a much more general one than it is commonly believed and that any situation where the initial conditions of a system can be represented as the superposition of eigenstates or eigenmodes leads to recurrences.