A two-level system swept through an avoided crossing: slow sweeps follow the adiabatic eigenstate; fast sweeps cause diabatic (non-adiabatic) transitions. Transition probability P = exp(-2πΩ²/|α|).
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Run simulation to see transition probability
LZ formula: P_diabatic = e^{-2πΩ²/|α|}. Adiabatic limit (slow α, large Ω): P→0, system stays in ground state. Sudden limit (fast α): P→1, no time to follow adiabatic path.