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تسجيل مستخدم جديدMode-Coupling Theory of the Glass Transition: A Primer
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Liesbeth M. C. Janssen
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Understanding the physics of glass formation remains one of the major unsolved challenges of condensed matter science. As a material solidifies into a glass, it exhibits a spectacular slowdown of the dynamics upon cooling or compression, but at the same time undergoes only minute structural changes. Among the numerous theories put forward to rationalize this complex behavior, Mode-Coupling Theory (MCT) stands out as the only framework that provides a fully first-principles-based description of glass phenomenology. This review outlines the key physical ingredients of MCT, its predictions, successes, and failures, as well as recent improvements of the theory. We also discuss the extension and application of MCT to the emerging field of non-equilibrium active soft matter
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ite-dimensional glass-forming systems, in particular supercooled liquids. The main difficulty for going beyond the mean-field treatment comes from the presence of diverging point-to-set spatial correlations. We introduce a variational low-temperature approximation scheme that allows us to account, at least in part, for the effect of these correlations. The outcome is an effective theory for the overlap fluctuations in terms of a random-field + random-bond Ising model with additional, power-law decaying, pair and multi-body interactions generated by the point-to-set correlations. This theory is much more tractable than the original problem. We check the robustness of the approximation scheme by applying it to a fully connected model already studied in the companion paper. We discuss the physical implications of this mapping for glass-forming liquids and the possibility it offers to determine the presence or not of a finite-temperature thermodynamic glass transition.
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We present an extensive treatment of the generalized mode-coupling theory (GMCT) of the glass transition, which seeks to describe the dynamics of glass-forming liquids using only static structural information as input. This theory amounts to an infin
ite hierarchy of coupled equations for multi-point density correlations, the lowest-order closure of which is equivalent to standard mode-coupling theory. Here we focus on simplified schematic GMCT hierarchies, which lack any explicit wavevector-dependence and therefore allow for greater analytical and numerical tractability. For one particular schematic model, we derive the unique analytic solution of the infinite hierarchy, and demonstrate that closing the hierarchy at finite order leads to uniform convergence as the closure level increases. We also show numerically that a similarly robust convergence pattern emerges for more generic schematic GMCT models, suggesting that the GMCT framework is generally convergent, even though no small parameter exists in the theory. Finally, we discuss how different effective weights on the high-order contributions ultimately control whether the transition is continuous, discontinuous, or strictly avoided, providing new means to relate structure to dynamics in glass-forming systems.
We numerically study the relaxation dynamics of several glass-forming models to their inherent structures, following quenches from equilibrium configurations sampled across a wide range of temperatures. In a mean-field Mari-Kurchan model, we find tha
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