title: Velocity autocorrelation of a free particle driven by a Mittag-Leffler noise: fractional dynamics and temporal behaviors.
abstract: We investigate the dynamical phase diagram of the generalized Langevin equation of the free particle driven by a Mittag-Leffler noise and show critical curves and a critical value of the exponent parameter of the Mittag-Leffler function that mark different dynamical regimes. By considering that the modeling of a Mittag-Leffer memory kernel corresponds to a power-law second-order memory kernel, we show that the generalized Langevin equation of the velocity autocorrelation function (VACF) is transformed in a fractional Langevin equation. In the superdiffusive case our results exhibit oscillations and negative correlations of the VACF that are not provided by the usual power-law noise model.
authors.affiliation: CRUB, Universidad Nacional del Comahue, Quintral 1250, 8400 Bariloche, Río Negro, Argentina and Extensión Áulica de la Universidad Tecnológica Nacional, 8400 Bariloche, Río Negro, Argentina.
authors.forename: A D
authors.initials: AD
authors.lastname: Viñales
authors.affiliation: CRUB, Universidad Nacional del Comahue, Quintral 1250, 8400 Bariloche, Río Negro, Argentina and Centro atomico Bariloche, CNEA/CONICET, Av. Bustillo Km 9.5, 8400 Bariloche, Río Negro, Argentina.
authors.forename: G H
authors.initials: GH
authors.lastname: Paissan