Generalized mode-coupling theory for mixtures of Brownian particles

Abstract

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Dynamics of supercooled liquids from static averaged quantities using machine learning

“…We see that at T > 0.6T mct the MLP produces excellent predictions even when it is trained for a different interaction potential. However the quality drops for very low temperature, when minute differences between the LJ and WCA structures are amplified to enormous differences in dynamics [31,43,44,[49][50][51] and configurational entropy [52][53][54]. In particular the model performs poorly when it is trained using the WCA potential and tested over the LJ data.…”

“…From a mathematical point of view, this equation takes as input the statistically-averaged static structure of the system, mainly through the static structure factor S(k) which is a function of the wave vector k. Using S(k) as the initial boundary condition, the memory equation can then be used to predict the time-dependent dynamics of the system, quantified by the intermediate scattering function F(k, t) at a given time t. The key bottleneck, however, is finding the exact memory function that governs the dynamics of F(k, t); this memory function should account for the dynamical slowdown of supercooled liquids, but its functional form is a priori unknown. After decades of intense research, scientists have been able to solve only approximations of this equation, like mode-coupling theory (MCT) [22,31,34,[36][37][38][39][40][41][42][43].…”

Many-Body Correlations Are Non-negligible in Both Fragile and Strong Glassformers

“…Recently, generalized mode-coupling theory (GMCT) has been developed as a systematic extension of MCT that adds in higher-order dynamic and static correlations [34][35][36][37][38]. Under certain conditions, the hierarchical GMCT framework is even able to account for relaxation behaviors other than the unrealistic power law noted above [39].…”

“…The key unknown part of Eq. ( 1) is the memory kernel K ð2nÞ , which GMCT hierarchically expands as a linear combination of the next-level correlators F ð2ðnþ1ÞÞ [34,[36][37][38]. That is,…”

“…It is clear now that the inputs to the GMCT framework are only S ð2Þ and c ð3Þ , with the latter only appearing in the vertices. To numerically solve the GMCT equations, we follow previous work [36][37][38] and apply a self-consistent closure for the multipoint dynamic density correlations at the highest level N, such that F ð2NÞ ðtÞ ≈ F ð2Þ ðtÞ× F ð2½N−1Þ ðtÞ (see Supplemental Material [47]). In the following, we report how the inclusion of c ð3Þ and the level N affect the liquid-glass transition for BHS and SiO 2 , as well as the predicted fragility of the latter.…”