Quantum Zeno & Anti-Zeno Crossover

Frequent measurement slows or accelerates decay depending on spectral density

Quantum Zeno effect: N measurements in time T → survival probability P = [cos²(Ωτ/2)]^N ≈ exp(−Ω²T τ/2) → 1 as τ→0. Anti-Zeno effect occurs when measurement interval τ ≈ 1/ω_max of spectral density — the decay is accelerated. The Zeno-to-Anti-Zeno crossover occurs at τ_crossover = τ_Z (the Zeno time). Spectral density J(ω) shape determines which regime dominates.