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We study the dynamics of density fluctuations in the steady state of anon-equilibrium system, the Zero-Range Process on a ring lattice. Measuring thetime series of the total number of particles in a \emph{segment} of thelattice, we find remarkable structures in the associated power spectra, namely,two distinct components of damped-oscillations. The essential origin of bothcomponents is shown in a simple pedagogical model. Using a more sophisticatedtheory, with an effective drift-diffusion equation governing the stochasticevolution of the local particle density, we provide reasonably good fits to thesimulation results. The effects of altering various parameters are explored indetail. Avenues for improving this theory and deeper understanding of the roleof particle interactions are indicated.

Power Spectra in a Zero-Range Process on a Ring: Total Occupation Number in a Segment