Mode-coupling theory

In this set of lecture notes we review the mode-coupling theory of the glass transition from several perspectives. First, we derive mode-coupling equations for the description of density fluctuations from microscopic considerations with the use the Mori–Zwanzig projection operator technique. We also derive schematic mode-coupling equations of a similar form from a field-theoretic perspective. We review the successes and failures of mode-coupling theory, and discuss recent advances in the applications of the theory.

[1]  W. Gotze,et al.  Dynamics of supercooled liquids and the glass transition , 1984 .

[2]  Thirumalai,et al.  Comparison between dynamical theories and metastable states in regular and glassy mean-field spin models with underlying first-order-like phase transitions. , 1988, Physical review. A, General physics.

[3]  E. Leutheusser.  Dynamical model of the liquid-glass transition , 1984 .

[4]  Wolfgang Götze,et al.  REVIEW ARTICLE: Recent tests of the mode-coupling theory for glassy dynamics , 1999 .

[5]  S. Glotzer,et al.  Time-dependent, four-point density correlation function description of dynamical heterogeneity and decoupling in supercooled liquids , 2000 .

[6]  Giorgio Parisi,et al.  On non-linear susceptibility in supercooled liquids , 2000, cond-mat/0005095.

[7]  G. Biroli,et al.  Diverging length scale and upper critical dimension in the Mode-Coupling Theory of the glass transition , 2004, cond-mat/0401260.

[8]  M. Mézard,et al.  Out of equilibrium dynamics in spin-glasses and other glassy systems , 1997, cond-mat/9702070.

[9]  G. Szamel.  Colloidal glass transition: beyond mode-coupling theory. , 2003, Physical review letters.

[10]  W. Kob.  Supercooled liquids, the glass transition, and computer simulations , 2002, cond-mat/0212344.

[11]  S. Glotzer,et al.  Spatial correlations of mobility and immobility in a glass-forming Lennard-Jones liquid. , 1998, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[12]  Steven J. Plimpton,et al.  DYNAMICAL HETEROGENEITIES IN A SUPERCOOLED LENNARD-JONES LIQUID , 1997 .

[13]  S. Nagel,et al.  Supercooled Liquids and Glasses , 1996 .

[14]  Marco Zoppi,et al.  Dynamics of the liquid state , 1994 .

[15]  S. Flach,et al.  TheA4 glass transition singularity , 1987 .

[16]  Higher-order glass-transition singularities in colloidal systems with attractive interactions. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  I. R. Mcdonald,et al.  Theory of simple liquids , 1998 .

[18]  Das,et al.  Fluctuating nonlinear hydrodynamics and the liquid-glass transition. , 1986, Physical review. A, General physics.

[19]  Steven J. Plimpton,et al.  STRINGLIKE COOPERATIVE MOTION IN A SUPERCOOLED LIQUID , 1998 .

[20]  Jean-Philippe Bouchaud,et al.  Mode-coupling approximations, glass theory and disordered systems , 1995, cond-mat/9511042.

[21]  A. Young,et al.  Spin glasses and random fields , 1997 .