6533b85ffe1ef96bd12c26cf
RESEARCH PRODUCT
Mode-coupling theory for multiple decay channels
Rolf SchillingSimon LangThomas Franoschsubject
Statistics and ProbabilityPhysicsClass (set theory)Statistical Mechanics (cond-mat.stat-mech)Maximum theoremFOS: Physical sciencesStatistical and Nonlinear PhysicsCovarianceCondensed Matter - Soft Condensed MatterSimple (abstract algebra)Mode couplingBrownian dynamicsSoft Condensed Matter (cond-mat.soft)Statistical physicsUniquenessRelaxation (approximation)Statistics Probability and UncertaintyCondensed Matter - Statistical Mechanicsdescription
We investigate the properties of a class of mode-coupling equations for the glass transition where the density mode decays into multiple relaxation channels. We prove the existence and uniqueness of the solutions for Newtonian as well as Brownian dynamics and demonstrate that they fulfill the requirements of correlation functions, in the latter case the solutions are purely relaxational. Furthermore, we construct an effective mode-coupling functional which allows to map the theory to the case of a single decay channel, such that the covariance principle found for the mode-coupling theory for simple liquids is properly generalized. This in turn allows establishing the maximum theorem stating that long-time limits of mode-coupling solutions can be calculated as maximal solutions of a fixed-point equation without relying on the dynamic solutions.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2013-12-20 |