User:Juto20/sandbox

A mostly unrelated thing is that the supercooled page should include more information about the \alpha-relaxation and \beta-relaxation process.

======================== ====== This is intended to be a future page on mode coupling theory, either to be created or merged with the page on mode coupling (which could arguable itself me merged either to normal mode or coupled mode theory).

To-do:


 * Some History
 * Discuss rough derivation from Mori-Zwanzig formalism?
 * Culigula-Kuchan equations a bit?
 * Gaussian approximation of density fluctuations

========================= ====== In physics, chemistry, and electrical engineering, mode coupling theory (also known as the mode coupling approximation, direction interaction approximation, and the self-consistent screening approximation ) is a perturbational method for approximating the dynamics of non-linear complex systems.

The word "mode" refers to eigenmodes of an idealized, "unperturbed", linear system. The superposition principle says that eigenmodes of linear systems are independent of each other: it is possible to excite or to annihilate a specific mode without influencing any other mode; there is no dissipation. In most real systems, however, there is at least some perturbation that causes energy transfer between different modes. This perturbation, interpreted as an interaction between the modes, is what is called "mode coupling". The mode coupling approximation is a method where one approximates these interactions by only considering pairwise interactions between modes, though generalizations which incorporate higher-order interactions have been considered.

The major applications of mode coupling theory has included providing accurate predictions of the behavior of supercooled fluids, colloids , and spin glasses. While it has seen mixed success in its original scope of understanding the glass transition, it still provides one of the only methods to predict the glass transition based only on microscopic interactions.