Asymptotically exact evaluation of $T_1$ and $T_2$ for a two-level system coupled to a bath with dichotomic colored noise

For a two-level system coupled stochastically to a bath with dichotomic colored noise the relaxation behavior is investigated. An exact numerical calculation shows that it can be described by two (longitudinal and transverse) relaxation rates only when correlations of the stochastic process decay rapidly enough as compared to the amplitude of the fluctuations. The numerical evaluation of the model also shows that the relation $T_2^{\mathrm{-}1}$≥0.5$T_1^{\mathrm{-}1}$, well known from textbooks, is generally not satisfied, in agreement with a recent fourth-order perturbative calculation. Finally, it is shown that this relaxation model for a δ-correlated bath is mathematically equivalent to the Haken-Strobl-Reineker model for the coupled coherent and incoherent motion of a quantum particle in the special case of transport in a dimer.