A Two-level system in a thermal bath

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Hello! I have a 2-level system, with the resonant frequency ##\omega_0## in a thermal bath, by which I mean that I have photons with mean frequency and standard deviation of frequency at a temperature ##T## given by:

$$<\omega> = \sigma_\omega = \frac{\pi^2}{6}\frac{k_B T}{\hbar}$$
I can assume that ##|\omega_0 - <\omega>| << \omega_0##. If I start in the ground state and I assume I am in the perturbative regime (i.e. only a very small population gets transferred to the excited state), how can I calculate the population transfer to the excited state as a function of time?
 
From the BCS theory of superconductivity is well known that the superfluid density smoothly decreases with increasing temperature. Annihilated superfluid carriers become normal and lose their momenta on lattice atoms. So if we induce a persistent supercurrent in a ring below Tc and after that slowly increase the temperature, we must observe a decrease in the actual supercurrent, because the density of electron pairs and total supercurrent momentum decrease. However, this supercurrent...

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