Holographic Fluctuation-Dissipation Relations in Finite Density Systems

Using real-time holography, we investigate fluctuation-dissipation relations in holographic systems at finite density. In the bulk, it corresponds to the study of scattering of a charged scalar field against a charged black hole background, leading to an exterior field theory outside the AdS Reissner-Nordstr\"om black hole. This theory captures dissipation (from infalling Quasi-normal modes) and fluctuations (from Hawking radiation). Here, we also develop a Witten diagrammatic framework for computing $n$-point functions for interacting charged scalars. From the boundary perspective, it gives real-time correlations of the dual CFT held at finite temperature and finite chemical potential. Our results yield (non)-linear holographic fluctuation-dissipation relations at small but finite density, which are shown to recover the correct behaviour in the zero-density limit.