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

TL;DR

This paper investigates the power spectra of density fluctuations in a non-equilibrium Zero-Range Process on a ring, revealing damped oscillations and modeling these phenomena with effective drift-diffusion equations.

Contribution

It introduces a detailed analysis of power spectra in a Zero-Range Process, including a simple pedagogical model and an effective theory that fits simulation data well.

Findings

Identification of two damped-oscillation components in power spectra

Effective drift-diffusion model successfully fits simulation results

Parameter variations explored to understand fluctuation behavior

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.