Landau-Zener Formula:
P_diabatic = e^(-2πΔ²/v)
P_adiabatic = 1 - P_dia
Δ = —
v = —
P_dia = —
P_adi = —
λ = —
P_diabatic = e^(-2πΔ²/v)
P_adiabatic = 1 - P_dia
Δ = —
v = —
P_dia = —
P_adi = —
λ = —
Two-level Hamiltonian H = ε(t)σ_z/2 + Δσ_x/2. Avoided crossing: eigenvalues repel by gap 2Δ. Landau-Zener: if swept fast (v≫Δ²) → diabatic transition. Slow → adiabatic (follows eigenstate). Berry phase accumulated at crossing = π for Δ→0.