Equilibrium states of generic quantum systems subject to periodic driving

When a closed quantum system is driven periodically with period $T$, it approaches a periodic state synchronized with the drive in which any local observable measured stroboscopically approaches a steady value. For integrable systems, the resulting behaviour is captured by a periodic version of a generalized Gibbs ensemble. By contrast, here we show that for generic non-integrable interacting systems, local observables become independent of the initial state entirely. Essentially, this happens because Floquet eigenstates of the driven system at quasienergy $\omega_\alpha$ consist of a mixture of the exponentially many eigenstates of the undriven Hamiltonian which are thus drawn from the entire extensive undriven spectrum. This is a form of equilibration which depends only on the Hilbert space of the undriven system and not on any details of its Hamiltonian.