Quantum Chaos — Kicked Rotor & Standard Map

The Chirikov standard map p_{n+1} = p_n + K sin(θ_n), θ_{n+1} = θ_n + p_{n+1} is the universal near-integrable Hamiltonian map. For K < K_c ≈ 0.9716 (Chirikov threshold), KAM tori survive; above K_c, global chaos appears. The quantum kicked rotor shows dynamical localization (Anderson localization in momentum space).

Parameters

Kick strength K 1.5 Num orbits 50 Iterations/orbit 200 Mode

Chirikov

K_c ≈ 0.9716

K/K_c: —

Phase: —

Poincaré section (θ,p) mod 2π
KAM tori = closed curves
Chaotic sea = scattered dots
Quantum: Husimi dist of |ψ⟩