Non-adiabatic transitions for random processes in a two-level system

Non-adiabatic transitions in two-level systems are investigated theoretically for a random time dependence of ?ω, the energy difference, between the levels. We assumed that ω = ω(x) and the coordinate x = x(t) is a random function of time. Diffusion and Poisson processes (both homogeneous and with a source) for x(t) were assumed. The cases of linear crossing terms (ω = γx) and non-linear terms (ω = ω _e exp (- αx) + ω₀) were considered. Values of the non-adiabatic transition probability per unit time were obtained by perturbation theory for ω₁τ _c ? 1 where τ _c is the correlation time and ω₁ is the off-diagonal matrix element.