Power spectra of TASEPs with a localized slow site

TL;DR

This study investigates how a localized slow site in TASEP affects the power spectra of particle occupancy, revealing that defect position influences oscillatory behaviors and system fluctuations through simulations and analytical modeling.

Contribution

It introduces a slow site into TASEP and analyzes its impact on power spectra and fluctuations, combining Monte Carlo simulations with a linearized Langevin approach.

Findings

Oscillations in power spectra disappear when defect is at the center.

Oscillations are restored when defect is off-center.

Defect position influences fluctuation dynamics and sublattice interactions.

Abstract

The totally asymmetric simple exclusion process (TASEP) with a localized defect is revisited in this article with attention paid to the power spectra of the particle occupancy N(t). Intrigued by the oscillatory behaviors in the power spectra of an ordinary TASEP in high/low density phase(HD/LD) observed by Adams et al. (2007 Phys. Rev. Lett. 99 020601), we introduce a single slow site with hopping rate q<1 to the system. As the power spectrum contains time-correlation information of the particle occupancy of the system, we are particularly interested in how the defect affects fluctuation in particle number of the left and right subsystems as well as that of the entire system. Exploiting Monte Carlo simulations, we observe the disappearance of oscillations when the defect is located at the center of the system. When the defect is off center, oscillations are restored. To explore the origin of such phenomenon, we use a linearized Langevin equation to calculate the power spectrum for the sublattices and the whole lattice. We provide insights into the interactions between the sublattices coupled through the defect site for both simulation and analytical results.