The Riccati equation bridges the two probability amplitudes in Landau-Zener transitions and pinpoints why the Markov approximation succeeds for one amplitude but fails for the other.
(79), of ηM we find the expres- sion ηM(−τ) = e−iϵτ 2 −τZ −τ0 dτ ′eiϵτ ′2 (113) which with the new integration variable ¯τ ≡ − τ ′ takes the form ηM(−τ) = e−iϵτ 2 τ0Z τ d¯τ eiϵ¯τ 2
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Hidden facts in Landau-Zener transitions revealed by the Riccati Equation
The Riccati equation bridges the two probability amplitudes in Landau-Zener transitions and pinpoints why the Markov approximation succeeds for one amplitude but fails for the other.