On long-time limit behavior of the solution of atom's master equation

We study long-time limit behavior of the solution of atom's master equation, for the first time we derive that the probability of the atom being in the α-th (α =j+1-j_z, j is the angular momentum quantum number, j_z is the z-component of angular momentum) state is (1-K/G)/1-(K/G)^2j+1(K/G)^α-1 as t→+∞, which coincides with the fact that when K/G > 1, the larger the α is, the larger probability of the atom being in the α-th state (the lower excited state). We also consider the case for some possible generalizations of the atomic master equation.