Mode-coupling theory for multiple decay channels
arXiv:1401.1420 · doi:10.1088/1742-5468/2013/12/P12007
Abstract
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.
14 pages
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- Long-time limit of correlation functions
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- Mode-coupling theory of the glass transition for colloidal liquids in slit geometry
- Static properties of quasi-confined hard-sphere fluids
- Dynamical properties of densely packed confined hard-sphere fluids
- Scaling equations for mode-coupling theories with multiple decay channels
- Dynamic properties of quasi-confined colloidal hard-sphere liquids near the glass transition
- Computer Simulations and Mode-Coupling Theory of Glass-Forming Confined Hard-Sphere Fluids
- Multiple character of non-monotonic size-dependence for relaxation dynamics in polymer-particle and binary mixtures
- Mode-coupling theory of the glass transition for a liquid in a periodic potential
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