Floquet Prethermalization

A periodically driven (Floquet) quantum system generically heats to infinite temperature. But at high driving frequency Ω, a prethermal plateau emerges — the system thermalizes to an effective Hamiltonian H* for an exponentially long time τ* ~ e^{Ω/J}, before eventually heating.

Ω/J = 15
A/J = 8
L = 8
J = 10
Floquet theorem: U(T) = e^{-iH_F T} | Effective Hamiltonian H* = H₀ + [H₁,H₂]/(2iΩ) + ...
Prethermal lifetime: τ* ~ exp(c·Ω/J) | Prethermal temp: T* set by initial energy in H*
At Ω→∞: heating suppressed — stable Floquet phases (Floquet-MBL, time crystals)