5 January, 2010 :
Lecture 2: Survey of theories of glassy behavior
Abstract
In my first lecture I will briefly discuss why a good knowledge of the properties of liquids is necessary in order to understand glasses. Subsequently I introduce the relevant quantities and observables that are used to describe the structural properties of liquids (radial distribution function, static structure factor, coordination number, ring statistics, ...). I then will discuss how the dynamic properties of liquids can be characterized by introducing the mean squared displacement of a tagged particle, the van Hove functions, the intermediate scattering functions, susceptibilities, the viscosity, and rotational correlation functions. Further concepts that will be discussed are the Stokes-Einstein and Debye-Stokes-Einstein relations and the vibrational density of states.
In the second lecture I will give a brief overview of the various approaches used to describe the properties of glass-forming systems. In particular I will discuss the continuous random network, random close packing, landscape models, Adam-Gibbs theory, free volume theory, rigidity percolation, mode coupling theory, replica approach, random first order theory and others.
References and Suggested Reading
- K. Binder and W. Kob "Glassy Materials and Disordered Solids: An Introduction to their Statistical Mechanics" (World Scientific, Singapore, 2005)
- G. Biroli and J. P. Bouchaud "The Random First-Order Transition Theory of Glasses: a critical assessment"; http://arxiv.org/pdf/0912.2542
- A. Cavagna, "Supercooled Liquids for Pedestrians"; Phys. Rep. 476, 51 (2009) http://arxiv.org/abs/0903.4264
- W. Götze, "Complex Dynamics of Glass-Forming Liquids: A Mode-Coupling Theory" (Oxford University Press, Oxford, 2009)
- J. P. Hansen and I.R. McDonald "Theory of simple liquids" (Academic Press, London, 2006)