Quantum Decoherence & Einselection

Decoherence rate γ: 0.2 System ω₀: 1.0 Init. θ (polar): 90° Init. φ (azimuth): 0°

Bloch |r|: —

Purity Tr(ρ²): —

Coherence |ρ₀₁|: —

Entropy S: —

Pointer basis: |0⟩,|1⟩

Lindblad master eq:

ρ̇ = -i[H,ρ] + γ(LρL†-½{L†L,ρ})

L = σ_z (dephasing)

Einselection: Environment selects "pointer states" — eigenstates of H_int that decohere least.

Off-diagonals decay:

|ρ₀₁(t)| = |ρ₀₁(0)|e^{-γt/2}

Coherence → 0, mixed state appears classical.