Nonergodicity parameter dynamic susceptibility

Close to the crossover temperature Tc, the solution of the idealized MCT equations can be expanded around the nonergodicity parameter fc at Tc and some generic laws can be derived. These leading-order results establish the so-called asymptotic laws of MCT, which can be regarded as generic features of the MCT dynamics at T > Tc. Because almost all experimental tests analyzed the susceptibility spectra in this frame, we are going to briefly summarize the laws [16,17,19]. Examples of tests against experiment are found in Section IV.E. 

Concerning the slow dynamics below the crossover temperature Tc, the predictive power of the theory seems to be rather limited. In particular, the emergence of intrinsic slow secondary processes, which seems to be associated with the dynamic crossover in the experimental spectra, is not contained even in the extended versions of the theory consequently, the slow dynamics spectrum is not reproduced correctly. In this respect, the extended theory introducing the hopping mechanism for describing the susceptibility minimum below Tc is misleading. On the other hand, the most prominent prediction of MCT below Tc is the anomaly of the nonergodicity parameter, which, as discussed, is found by different model-independent approaches. However, within the framework of MCT, this anomaly is closely connected with the appearance of a so-called knee feature in the spectral shape of the fast dynamics spectrum below Tc. This feature, however, has not been identified experimentally in molecular liquids, and only indications for its existence are observed in colloidal systems [19]. In molecular systems, merely a more or less smooth crossover to a white noise spectrum has been reported in some cases [183,231,401]. Thus, it may be possible that the knee phenomenon is also smeared out. 

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