A Monte Carlo investigation of noise and diffusion of particles exhibiting asymmetric exclusion processes

We have carried out a simulative investigation of the inter-relations between noise and diffusion in barrier limited transport for the ASEP condition. For the case of the closed ring, since the number of particles is fixed, only the noise related to velocity fluctuations is present. Here, the diffusion coefficient obtained from the Fick’s law is explicitly related to current noise, both in the presence and in the absence of the ASEP. Therefore, evidence is provided for the existence of a generalized Nyquist–Einstein relation allowing the determination of diffusion from a noise measurement or vice versa. The correlations introduced by ASEP are found to be responsible for the dependence of diffusion upon the inverse square root of the device length. For the case of the open linear chain the diffusion coefficient obtained from Fick’s law is no longer related to the current noise, which now contains contributions coming from velocity, number, and their cross-correlations. Here the diffusion coefficient is found to be independent of the number of sites, but to depend on the strength of the correlation that is ultimately controlled by the carrier density. In this case, owing to the open boundaries, the number of particles is not constant through the simulation, and the charge density can fluctuate in time. Finally, we remark that analytical results concerning 1,2 in the presence of ASEP are correctly interpreted only if 1,2 are related to the variance in the number of carriers that entered up to time t into the system from a given cross-sectional area and not to a diffusion constant.