The correlation function for a two-level atom in contact with a reservoir of photons at temperature T is (I'm using natural units):
C_R(\tau)\propto PolyGamma[4, 1-i (\tau/\beta)],
where \beta=1/T.
A plot for T=300K shows that the reservoir decay time is \tau_R~0.25*10^{-13}s, whereas for T=10K, \tau_R~1.5*10^{-12}s. Both times are much less that the decay of an atom t_s~10^{-8}s, therefore, it looks like the Markov approximation works for low-temperatures. Nevertheless, in the literature, I find that such approximation fails when temperature decreases.
What is wrong with my logic?
Thanks.
The bath of fluctuations that describes the decay of an atom doesn’t behave like a bath of photons.
The quantum thermal machines often relies on master equations.It widely used, but often criticized and local approach for sub-systems locally coupled to thermal baths. The thermal baths couple to degrees of freedom . There are conceptually different approaches used in situations out of thermal equilibrium. Under consider thermodynamically relevant observables, such as heat currents, as well as the quantum state . In particular, for weak intersystem coupling, the local approach agrees with the exact solution, whereas the global approach fails for non-equilibrium situations.
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