Abstract
The generalised multilevel Landau–Zener problem is solved by applying the density matrix technique within the framework of nonstationary perturbation theory. The exact survival probability is achieved as a proof of the Brundobler–Elzer hypothesis (Brundobler and Elzer (1993) [38]). The effect of classical Gaussian noise is investigated by averaging the solution over the noise realisation. A generalised formula for slow noise-induced transition probability is obtained and found to agree exactly with all known results. Exact results are reported for the Demkov–Osherov model in the slow and fast noise limits. Thermal transition probabilities are obtained via the activation Arrhenius law and observed to tailor a qubit from thermal decoherence.
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