Decoherence rate in an exactly solvable model of an open quantum system

The well-known exactly solvable model of decoherence in an open quantum system is considered. Despite its fame, a detailed analysis of the dependence of the decoherence rate on the spectral function (namely, on its asymptotic behavior at low frequencies) has not yet been available. The report is devoted to filling this gap. The results also allow us to discuss the limits of applicability of the Markov approximation for this model.