title: Transport and fluctuation-dissipation relations in asymptotic and preasymptotic diffusion across channels with variable section.
abstract: We study the asymptotic and preasymptotic diffusive properties of Brownian particles in channels whose section varies periodically in space. The effective diffusion coefficient D(eff) is numerically determined by the asymptotic behavior of the root mean square displacement in different geometries, considering even cases of steep variations of the channel boundaries. Moreover, we compared the numerical results to the predictions from the various corrections proposed in the literature to the well known Fick-Jacobs approximation. Building an effective one-dimensional equation for the longitudinal diffusion, we obtain an approximation for the effective diffusion coefficient. Such a result goes beyond a perturbation approach, and it is in good agreement with the actual values obtained by the numerical simulations. We discuss also the preasymptotic diffusion which is observed up to a crossover time whose value, in the presence of strong spatial variation of the channel cross section, can be very large. In addition, we show how the Einstein's relation between the mean drift induced by a small external field and the mean square displacement of the unperturbed system is valid in both asymptotic and preasymptotic regimes.
authors.affiliation: Dipartimento di Fisica Università di Roma "Sapienza," Piazzale Aldo Moro 2, I-00185 Roma, Italy.
authors.forename: Giuseppe
authors.initials: G
authors.lastname: Forte
authors.affiliation: CNR-Istituto dei Sistemi Complessi (ISC), Via dei Taurini 19, I-00185 Roma, Italy.
authors.forename: Fabio
authors.initials: F
authors.lastname: Cecconi
authors.affiliation: Dipartimento di Fisica Università di Roma "Sapienza," Piazzale Aldo Moro 2, I-00185 Roma, Italy and CNR-Istituto dei Sistemi Complessi (ISC), Piazzale Aldo Moro 2, I-00185 Roma, Italy.
authors.forename: Angelo
authors.initials: A
authors.lastname: Vulpiani