title: Mode-coupling theory of the glass transition for confined fluids.
abstract: We present a detailed derivation of a microscopic theory for the glass transition of a liquid enclosed between two parallel walls relying on a mode-coupling approximation. This geometry lacks translational invariance perpendicular to the walls, which implies that the density profile and the density-density correlation function depends explicitly on the distances to the walls. We discuss the residual symmetry properties in slab geometry and introduce a symmetry adapted complete set of two-point correlation functions. Since the currents naturally split into components parallel and perpendicular to the walls the mathematical structure of the theory differs from the established mode-coupling equations in bulk. We prove that the equations for the nonergodicity parameters still display a covariance property similar to bulk liquids.
authors.affiliation: Institut für Theoretische Physik, Universität Erlangen-Nürnberg, Staudtstraße 7, 91058 Erlangen, Germany.
authors.forename: Simon
authors.initials: S
authors.lastname: Lang
authors.forename: Rolf
authors.initials: R
authors.lastname: Schilling
authors.forename: Vincent
authors.initials: V
authors.lastname: Krakoviack
authors.forename: Thomas
authors.initials: T
authors.lastname: Franosch