Power spectra of TASEPs with a localized slow site

The totally asymmetric simple exclusion process (TASEP) with a localized defect is revisited in this paper 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 (HD/LD) phases observed previously, we introduce a single slow site with hopping rate q < 1 to the system. As the power spectrum contains time-correlation information on 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 a 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