Soft Condensed Matter, Biological Physics Experiment & Statistical Physics Seminars

Beginning from the foundation some assumption of ergodicity of Statistical Mechanics, we outline how ergodicity is lost in phase transitions. We contrast this with the more complex behaviour when ergodicity is lost in scenarios such as the glass 'transition'. We conclude that the most hopeful approach, in general, is to study such problems directly using Newtons equations, or dynamics, rather than probability distributions, such as that introduced by Boltzmann. The reason is that we do not know how to calculate probability distributions for systems that lose their ergodicity in complicated ways.

    Even so,we note that it is difficult to carry out molecular dynamics calculations near glass transitions because of the very long time scales involved. There are are two alternative approaches open to theorists, and the experimentalists that they work with.

    The first is to carry out analogue experiments of 'molecular dynamics' using dynamical confocal microscopy, such as experiments of Weeks and Weitz for colloidal particles. These experiments are discussed briefly, and it is discussed how they can be analysed using the tools of theory. It is also shown how, with these and experiments carried out in Edinburgh, experimental measurements may bring forward the level of theory.

    The second approach is to apply some approximation scheme to Newtons equations, and then try to solve the theory. We show, in outline form, how this may be done, and then comment that a simple approximation to the scheme yields the well known Mode Coupling Theory (MCT) that is currently used to interpret the arrest transition of colloidal 'glasses'.

   Applications of MCT to systems with, for example, attractive potentials such as those in depletion-dominated colloidal systems studied in Edinburgh, and elsewhere are introduced, and discussed, if time permits.

The seminar, in order to remain as accessible as possible, will where possible avoid technical detail in any of the topics, though further references will be given if necessary to permit the non-specialist to probe further.

Reference:
[1] K. Dawson et al, Phys. Rev. E 63, 11401 (2000).