Power spectra in a zero-range process on a ring: total occupation number in asegment

Abstract

We study the dynamics of density fluctuations in the steady state of a non-equilibriumsystem, the zero-range process on a ring lattice. Measuring the time series of the totalnumber of particles in a segment of the lattice, we find remarkable structures in theassociated power spectra, namely, two distinct components of damped oscillations. Theessential origin of both components is shown in a simple pedagogical model. Using a moresophisticated theory, with an effective drift–diffusion equation governing the stochasticevolution of the local particle density, we provide reasonably good fits to the simulationresults. The effects of altering various parameters are explored in detail. Avenues forimproving this theory and deeper understanding of the role of particle interactions areindicated.