Generalized Bloch equations and dissipation of longitudinal magnetic-field energy

For a spin-1 / 2 coupled to a Gaussian heat bath in the presence of an external magnetic field, we generalize the Bloch equations to the non-Markovian case. Using this generalization as the base, we show that the time-varying component of the magnetic field parallel to its constant part is absorbed by the spin system, especially at high temperatures of the heat bath. For the spectral density and dispersion of longitudinal spin fluctuations, we obtain expressions that are in good agreement with known results.