title: Underdamped scaled Brownian motion: (non-)existence of the overdamped limit in anomalous diffusion.
abstract: It is quite generally assumed that the overdamped Langevin equation provides a quantitative description of the dynamics of a classical Brownian particle in the long time limit. We establish and investigate a paradigm anomalous diffusion process governed by an underdamped Langevin equation with an explicit time dependence of the system temperature and thus the diffusion and damping coefficients. We show that for this underdamped scaled Brownian motion (UDSBM) the overdamped limit fails to describe the long time behaviour of the system and may practically even not exist at all for a certain range of the parameter values. Thus persistent inertial effects play a non-negligible role even at significantly long times. From this study a general questions on the applicability of the overdamped limit to describe the long time motion of an anomalously diffusing particle arises, with profound consequences for the relevance of overdamped anomalous diffusion models. We elucidate our results in view of analytical and simulations results for the anomalous diffusion of particles in free cooling granular gases.
authors.affiliation: Institut für Physik, Humboldt-Universität zu Berlin, Newtonstrasse 15, 12489 Berlin, Germany.|Faculty of Physics, M.V.Lomonosov Moscow State University, Moscow, 119991, Russia.
authors.forename: Anna S
authors.initials: AS
authors.lastname: Bodrova
authors.affiliation: Akhiezer Institute for Theoretical Physics, Kharkov Institute of Physics and Technology, Kharkov 61108, Ukraine.|Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany.|Department of Physics &Astronomy, University of Padova, 35122 Padova, Italy.
authors.forename: Aleksei V
authors.initials: AV
authors.lastname: Chechkin
authors.affiliation: Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany.
authors.forename: Andrey G
authors.initials: AG
authors.lastname: Cherstvy
authors.affiliation: Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany.|Department of Physics, Shahid Beheshti University, G.C., Evin, Tehran 19839, Iran.
authors.forename: Hadiseh
authors.initials: H
authors.lastname: Safdari
authors.affiliation: Institut für Physik, Humboldt-Universität zu Berlin, Newtonstrasse 15, 12489 Berlin, Germany.
authors.forename: Igor M
authors.initials: IM
authors.lastname: Sokolov
authors.affiliation: Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany.
authors.forename: Ralf
authors.initials: R
authors.lastname: Metzler