Dresden 2014 – wissenschaftliches Programm
DY 7.5: Vortrag
Montag, 31. März 2014, 16:00–16:15, ZEU 146
Existence of glass-form factors — •Thomas Franosch — Institut für Theoretische Physik, Leopold-Franzens-Universität Innsbruck, A-6020 Innsbruck, Austria
A hallmark of the glass transition is the slow structural relaxation of a quasi-arrested structure. As an idealization the dynamics is considered to become non-ergodic directly at the glass transition such that all auto-correlation function coupling to the structural relaxation exhibit finite non-trivial long-time limits often referred to as glass-form factors or nonergodicity parameters. Simultaneously, the theory of stochastic processes in the framework of probability theory imposes quite stringent conditions on the class of correlation functions. The existence of a finite limit at long times is then connected to the properties of the associated spectral measure, and in general correlation functions can either oscillate forever, display quasi-periodic behavior, or even intermittent behavior. While for purely relaxation dynamics, e.g. Brownian dynamics, the existence of a long-time limit is trivial, the situation for the case of Newtonian dynamics has been elusive so far.
In this talk I elaborate conditions covering a broad class of theoretical approaches that guarantee the existence of a long-time limit. As a special case I show that the mode-coupling theory of the glass transition belongs to that class. As an outlook I briefly discuss the case of multiple decay channels relevant for molecular or confined systems.