Power-law behavior in the power spectrum induced by Brownian motion of a domain wall

TL;DR

This paper demonstrates that the Brownian motion of a domain wall in a finite system causes a characteristic power-law spectrum, with theoretical predictions matching numerical results in the TASEP model.

Contribution

It introduces a theoretical explanation for the power-law behavior in the power spectrum caused by domain wall Brownian motion, validated by numerical simulations.

Findings

Power spectrum exhibits a $requency^{-3/2}$ decay.

Theoretical predictions agree with numerical simulations.

Effective in the frequency range dominated by domain wall motion.

Abstract

We show that Brownian motion of a one-dimensional domain wall in a large but finite system yields a $\omega^{-3/2}$ power spectrum. This is successfully applied to the totally asymmetric simple exclusion process (TASEP) with open boundaries. An excellent agreement between our theory and numerical results is obtained in a frequency range where the domain wall motion dominates and discreteness of the system is not effective.