The optical Bloch equation for the finite-temperature fluctuations

In this work, I analyze the quantum fluctuations and the thermal fluctuations in the framework of quantum mechanics. Being recognized as incoherent perturbations with different features, fluctuations of these two types lead to dissipative terms in the optical Bloch equations. The method allows one to use the optical Bloch equation to analyze time-dependent processes in the finite-temperature fluctuations. The numerical results show that the deexcitation is the limit of the equilibration at zero temperature. The impact of the fluctuations on the coherent excitations are also discussed.