TY - JOUR

T1 - Generalized mode-coupling theory of the glass transition

T2 - schematic results at finite and infinite order

AU - Janssen, L.M.C.

AU - Mayer, P.

AU - Reichman, D.R.

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

KW - Correlation functions (theory)

KW - Mode coupling theory

KW - Slow relaxation and glassy dynamics

UR - http://www.scopus.com/inward/record.url?scp=85013899078&partnerID=8YFLogxK

U2 - 10.1088/1742-5468/2016/05/054049

DO - 10.1088/1742-5468/2016/05/054049

M3 - Article

AN - SCOPUS:85013899078

VL - 2016

JO - Journal of Statistical Mechanics : Theory and Experiment

JF - Journal of Statistical Mechanics : Theory and Experiment

SN - 1742-5468

IS - 5

M1 - 054049

ER -