  We discuss the physics of sound propagation and charge diffusion in a plasma
with non-vanishing charge density. Our analysis culminates the program
initiated in arXiv:2108.03244 to construct an open effective field theory of
low-lying modes of the stress tensor and charge current in such plasmas. We
model the plasma holographically as a Reissner-Nordstrom-AdS black hole, and
study linearized fluctuations of longitudinally polarized scalar gravitons and
photons in this background. We demonstrate that the perturbations can be
decoupled and repackaged into the dynamics of two designer scalars, whose
gravitational coupling is modulated by a non-trivial dilatonic factor. The
holographic analysis allows us to isolate the phonon mode from the charge
diffusion mode, and identify the combination of currents that corresponds to
each of them. We use these results to obtain the real-time Gaussian effective
action, which includes both the retarded response and the associated stochastic
(Hawking) fluctuations, accurate to quartic order in gradients.

High Energy Physics - Theory;Statistical Mechanics;General Relativity and Quantum Cosmology