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Article overview
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Generalized mode-coupling theory of the glass transition: schematic results at finite and infinite order | | Liesbeth M. C. Janssen
; Peter Mayer
; David R. Reichman
; | | Date: |
26 Oct 2015 | | Abstract: | 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 infinite 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. | | Source: | arXiv, 1510.7636 | | Services: | Forum | Review | PDF | Favorites | |
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