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

We study the dynamics of density fluctuations in the steady state of a non-equilibrium system, the Zero-Range Process on a ring lattice. Measuring the time series of the total number of particles in a \emph{segment} of the lattice, we find remarkable structures in the associated power spectra, namely, two distinct components of damped-oscillations. The essential origin of both components is shown in a simple pedagogical model. Using a more sophisticated theory, with an effective drift-diffusion equation governing the stochastic evolution of the local particle density, we provide reasonably good fits to the simulation results. The effects of altering various parameters are explored in detail. Avenues for improving this theory and deeper understanding of the role of particle interactions are indicated.
Comment: 21 pages, 15 figures