Role of the pair correlation function in the dynamical transition predicted by mode coupling theory - Nandi, Manoj Kumar; Banerjee, Atreyee; Dasgupta, Chandan; Bhattacharyya, Sarika Maitra (Physical Review Letters, 2017)
In a recent study, we have found that for a large number of systems the configurational entropy at the pair level S-c2, which is primarily determined by the pair correlation function, vanishes at the dynamical transition temperature T-c. Thus, it appears that the information of the transition temperature is embedded in the structure of the liquid. In order to investigate this, we describe the dynamics of the system at the mean field level and, using the concepts of the dynamical density functional theory, show that the dynamical transition temperature depends only on the pair correlation function. Thus, this theory is similar in spirit to the microscopic mode coupling theory (MCT). However, unlike microscopic MCT, which predicts a very high transition temperature, the present theory predicts a transition temperature that is similar to T-c. This implies that the information of the dynamical transition temperature is embedded in the pair correlation function.

Comparative study of a class of mean field theories of the glass transition - Saha, Indranil; Nandi, Manoj Kumar; Dasgupta, Chandan; Bhattacharyya, Sarika Maitra (Journal of Statistical Mechanics-Theory and Experiment, 2019)
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.
Keywords: aging; etc); glasses (colloidal; glassy dynamics; mode coupling theory; Polymer; slow relaxation

Thermodynamics and its correlation with dynamics in a mean-field model and pinned systems: a comparative study using two different methods of entropy calculation - Nandi, Ujjwal Kumar; Patel, Palak; Moid, Mohd; Nandi, Manoj Kumar; Sengupta, Shiladitya; Karmakar, Smarajit; Maiti, Prabal K.; Dasgupta, Chandan; Bhattacharyya, Sarika Maitra (Journal of Chemical Physics, 2022)
A recent study introduced a novel mean-field model system where each particle over and above the interaction with its regular neighbors interacts with k extra pseudo-neighbors. Here, we present an extensive study of thermodynamics and its correlation with the dynamics of this system. We surprisingly find that the well-known thermodynamic integration (TI) method of calculating the entropy provides unphysical results. It predicts vanishing of the configurational entropy at temperatures close to the onset temperature of the system and negative values of the configurational entropy at lower temperatures. Interestingly, well below the temperature at which the configurational entropy vanishes, both the collective and the single-particle dynamics of the system show complete relaxation. Negative values of the configurational entropy are unphysical, and complete relaxation when the configurational entropy is zero violates the prediction of the random first-order transition theory (RFOT). However, the entropy calculated using the two-phase thermodynamics (2PT) method remains positive at all temperatures for which we can equilibrate the system, and its values are consistent with RFOT predictions. We find that with an increase in k, the difference in the entropy computed using the two methods increases. A similar effect is also observed for a system where a randomly selected fraction of the particles are pinned in their positions in the equilibrated liquid. We show that the difference in entropy calculated via the 2PT and TI methods increases with pinning density.