Quantum resonance of the kicked rotor ($⟨K{⟩}_N={\hslash }^2{\eta }^2{N}^2/(4I)$)

When the free angular-momentum phases all recur at the driving period, successive identical kicks add coherently. For the full revival $\hslash T/(2I)=2\pi$ and an initial zero-angular-momentum state, the kinetic energy after $N$ kicks is ${\hslash }^2{\eta }^2{N}^2/(4I)$. This ballistic law is specific to the stated resonance and boundary conditions.