title: Glassy dynamics in confinement: planar and bulk limits of the mode-coupling theory.
abstract: We demonstrate how the matrix-valued mode-coupling theory of the glass transition and glassy dynamics in planar confinement converges to the corresponding theory for two-dimensional (2D) planar and the three-dimensional bulk liquid, provided the wall potential satisfies certain conditions. Since the mode-coupling theory relies on the static properties as input, the emergence of a homogeneous limit for the matrix-valued intermediate scattering functions is directly connected to the convergence of the corresponding static quantities to their conventional counterparts. We show that the 2D limit is more subtle than the bulk limit, in particular, the in-planar dynamics decouples from the motion perpendicular to the walls. We investigate the frozen-in parts of the intermediate scattering function in the glass state and find that the limits time t→∞ and effective wall separation L→0 do not commute due to the mutual coupling of the residual transversal and lateral force kernels.
authors.affiliation: Institut für Theoretische Physik, Leopold-Franzens-Universität Innsbruck, Technikerstraße 25/2, A-6020 Innsbruck, Austria.
authors.forename: Simon
authors.initials: S
authors.lastname: Lang
authors.affiliation: Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudinger Weg 7, D-55099 Mainz, Germany.
authors.forename: Rolf
authors.initials: R
authors.lastname: Schilling
authors.affiliation: Institut für Theoretische Physik, Leopold-Franzens-Universität Innsbruck, Technikerstraße 25/2, A-6020 Innsbruck, Austria.
authors.forename: Thomas
authors.initials: T
authors.lastname: Franosch