@article {47173,
	title = {Comparative study of a class of mean field theories of the glass transition},
	journal = {Journal of Statistical Mechanics-Theory and Experiment},
	volume = {2019},
	year = {2019},
	month = {AUG},
	pages = {084008},
	type = {Article},
	abstract = {<p>In a recently developed microscopic mean field theory, we have shown that the dynamics of a system, when described only in terms of its pair structure, can predict the correct dynamical transition temperature. Further, the theory predicted the difference in dynamics of two systems (the Lennard-Jones and the Weeks-Chandler-Andersen) despite them having quite similar structures. This is in contrast to the Schweizer-Saltzman (SS) formalism which predicted the dynamics of these two systems to be similar. The two theories although similar in spirit have certain differences. Here we present a comparative study of these two formalism to find the origin of the difference in their predictive power. We show that not only the dynamics in the potential energy surface, as described by our earlier study, but also that in the free energy surface, like in the SS theory, can predict the correct dynamical transition temperature. Even an approximate one component version of our theory, similar to the system used in the SS theory, can predict the transition temperature reasonably well. Interestingly, we show here that despite the above mentioned shortcomings the SS theory can actually predict the correct transition temperatures. Thus microscopic mean field theories of this class which express dynamics in terms of the pair structure of the liquid while being unable to predict the actual dynamics of the system are successful in predicting the correct dynamical transition temperature.</p>
},
	keywords = {aging, etc), glasses (colloidal, glassy dynamics, mode coupling theory, Polymer, slow relaxation},
	issn = {1742-5468},
	doi = {10.1088/1742-5468/ab3115},
	author = {Saha, Indranil and Nandi, Manoj Kumar and Dasgupta, Chandan and Bhattacharyya, Sarika Maitra}
}
@article {46964,
	title = {Continuous time random walk concepts applied to extended mode coupling theory: a study of the Stokes? Einstein breakdown},
	journal = {Journal of Physics-Condensed Matter},
	volume = {32},
	year = {2020},
	month = {FEB},
	pages = {064001},
	type = {Article},
	abstract = {<p>In an attempt to extend the mode coupling theory (MCT) to lower temperatures, some years back an Unified theory was proposed which within the MCT framework incorporated the activated dynamics via the random first order transition theory (RFOT). The theory successfully showed that there is hopping induced diffusive dynamics and the modified MCT coupled to the activated motion continues till low temperatures. Here we show that the theory although successful in describing other properties of supercooled liquids is unable to capture the Stokes?Einstein breakdown. We then show using continuous time random work (CTRW) formalism that the Unified theory is equivalent to a CTRW dynamics in presence of two waiting time distributions. It is known from earlier work on CTRW that in such cases the total dynamics is dominated by the fast motion. This explains the failure of the Unified theory in predicting the SE breakdown as both the structural relaxation and the diffusion process are described by the comparatively fast MCT like dynamics. The study also predicts that other forms of extended MCT with Markovian hopping kernel will face a similar issue. We next modify the Unified theory by applying the concept of renewal theory, usually used in CTRW models where the distribution has a long tail. According to this theory the first jump given by the persistent time is slower than the subsequent jumps given by the exchange time. We first show that for systems with two waiting time distributions even when both the distributions are exponential the persistent time is larger than the exchange time. We also identify the persistent time with the slower activated process. The extended Unified theory can now explain the SE breakdown. In this extended theory at low temperatures the structural relaxation is described by the activated dynamics whereas the diffusion is primarily determined by the MCT like dynamics leading to a decoupling between them. We also calculate a dynamic lengthscale from the wavenumber dependence of the relaxation time. We find that this dynamic length scale grows faster than the static length scale.</p>
},
	keywords = {continuous time random walk, mode coupling theory, Stokes?Einstein breakdown},
	issn = {0953-8984},
	doi = {10.1088/1361-648X/ab50d4},
	author = {Nandi, Manoj Kumar and Bhattacharyya, Sarika Maitra}
}
