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The thermalization of a two-level atom in a planar dielectric system out of thermal equilibrium

We study the thermalization of an elementary quantum system modeled by a two-level atom interacting with stationary electromagnetic fields out of thermal equilibrium near a dielectric slab. The slab is held at a temperature different from that of the region where the atom is located. We find that when the slab is a nonabsorbing and nondispersive dielectric of a finite thickness $ d$, no out of thermal equilibrium effects appear as far as the thermalization of the atom is concerned, and a finite thick dielectric slab with a tiny imaginary part in the relative permittivity $\operatorname{Im} ε$ behaves like a half space dielectric substrate if $\frac{\operatorname{Im} ε}{\sqrt{\operatorname{Re}ε-1}} \frac{d}{λ_0} > 1$ is satisfied, where $λ_0$ is the transition wavelength of the atom. This condition can serve as a guide for an experimental verification, using a dielectric substrate of a finite thickness, of the effects that arise from out of thermal equilibrium fluctuations with a half-space (infinite thickness) dielectric.