Environment-Induced Renormalization of Molecular Polarizabilities

The electromagnetic environment modifies atomic properties through self-energy corrections arising from vacuum-field fluctuations shaped by material boundaries. While such effects are commonly discussed in terms of energy level shifts and decay rates, their influence on atomic response functions has received much less attention. Here, we investigate how environment-induced self-energy corrections renormalize the dynamic polarizability of an atom. Using macroscopic quantum electrodynamics, we analyze a hydrogen atom at the center of a spherical vacuum cavity embedded in a dielectric medium. The cavity-induced Lamb shifts of the atomic levels propagate into the frequency-dependent polarizability through the sum-over-states representation. We find that cavity confinement shifts absorptive resonances, modifies their amplitudes, and can generate additional geometry-induced spectral features within the finite range of cavity radii. The polarizability along the imaginary-frequency axis remains well-behaved, consistent with a passive electromagnetic environment. These results demonstrate that structured electromagnetic environments can qualitatively reshape atomic response functions and provide a route toward geometry-aware descriptions of molecular polarizabilities in complex media.