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

Abstract

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.

21 pages, 15 figures

References in corpus (5)

• Dynamics of the condensate in zero-range processes
• Tagged Particle Correlations in the Asymmetric Simple Exclusion Process: Finite Size Effects
• Power Spectra of the Total Occupancy in the Totally Asymmetric Simple Exclusion Process
• Finite-size effects on the dynamics of the zero-range process
• Zero-range process with long-range interactions at a T-junction