Momentum Distribution |ψ(m)|²
⟨p²⟩ vs kicks (classical vs quantum)
Kicks: 0
The quantum kicked rotor is a paradigm of quantum chaos. Classically (K > 4.97),
the standard map shows chaotic diffusion: ⟨p²⟩ ∝ t (diffusion constant D≈K²/2).
Quantum mechanically, interference suppresses diffusion after a localization time t* ∼ D/ℏ²,
and the momentum distribution freezes into an exponential profile — dynamical localization,
the quantum analog of Anderson localization. Increase K to see faster diffusion; decrease ℏ_eff
to see the classical limit emerge.