Hamiltonian
Simulation
Kick #: 0
Lin. entropy S: 0.000
Regime: —
Husimi Q-function on the Bloch sphere + linear entropy vs. kick number
The kicked top Hamiltonian: H = p·Jy + (κ/2j)·Jz²·Σδ(t−n). Between kicks: free precession. At each kick: nonlinear rotation about z.
The Husimi Q-function Q(θ,φ) = |⟨θ,φ|ψ⟩|² visualises the quantum state on the Bloch sphere as a stereographic projection. For small κ (regular), Q stays localised near classical stable points. For κ > κ_c ≈ 2.5, classical chaos emerges and quantum spreading generates entanglement rapidly.
Linear entropy S_L = 1 − Tr(ρ_A²) measures bipartite entanglement when the spin-j system is split into two subsystems. In the chaotic regime, S_L saturates at the Page value — a direct quantum signature of classical chaos.