The mode coupling theory of structural relaxations

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Abstract
The basic ideas and approximations underlying the derivation of the mode coupling theory of structural relaxation in simple liquids are summarized. We explain why in disordered many particle systems the infinite set of density fluctuation products constitutes slow modes whose interactions lead to bifurcation singularities. The singularities are connected with the appearance of spontaneous arrest of particle distributions in ideal glass states. These constitute an almost frozen potential landscape for the phonon assisted transport processes, which restore ergodicity in strongly supercooled or super-compressed liquids. Some concepts needed for a description of structural relaxation are explained: glass transition singularities, non-ergodicity parameters, critical decay laws, separation parameters, critical temperature T c or density n c and α– and β–relaxation. It is emphasized that there are universality classes for the dynamics where the correlation functions within certain windows can be specified by a few number of parameters. Thereby it is shown that the theory can provide results for a quantitative description of experiments also for very complicated systems like polymers.

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