Quantum Kicked Rotor

Quantum chaos & dynamical localization — classical diffusion vs. quantum freezing

Parameters

Observables

⟨p²⟩ (quantum)
⟨p²⟩ (classical)
Kick #0
Loc. length ξ

Physics

The kicked rotor is governed by:

H = p²/2 + K cos(θ) Σ δ(t−n)

Classically: For K > 0.97 (Chirikov threshold), motion is chaotic and ⟨p²⟩ ∝ t (diffusion).

Quantum: Interference freezes diffusion after a localization time t* ~ ξ. ⟨p²⟩ saturates — dynamical localization, analogous to Anderson localization in 1D.

Localization length: ξ ~ K²/2ℏ²