Friday, December 16, 2011

Universality and "glassy" physics

One remarkable aspect of Nature is the recurrence of certain mathematically interesting motifs in different contexts.  When we see a certain property or relationship that shows up again and again, we tend to call that "universality", and we look for underlying physical reasons to explain its reappearance in many apparently disparate contexts.  A great review of one such type of physics was posted on the arxiv the other day. 

Physicists commonly talk about highly ordered, idealized systems (like infinite, perfectly periodic crystals), because often such regularity is comparatively simple to describe mathematically.  The energy of such a crystal is nicely minimized by the regular arrangement of atoms.   At the other extreme are very strongly disordered systems.  These disordered systems are often called "glassy" because structural glasses (like the stuff in your display) are an example.  In these systems, disorder dominates completely; the "landscape" of energy as a function of configuration is a big mess, with many local minima - a whole statistical distribution of possible configurations, with a whole distribution of energy "barriers" between them.  Systems like that crop up all the time in different contexts, and yet share some amazingly universal properties.  One of the most dramatic is that when disturbed, these systems take an exceedingly long time to respond completely.  Some parts of the system respond fast, others more slowly, and when you add them all together, you get total responses that look logarithmic in time (not exponential, which would indicate a single timescale for relaxation).  For example, the deformation response of crumpled paper (!) shows a relaxation that is described by constant*log(t) for more than 6 decades in time!  Likewise, the speed of sound or dielectric response in a glass at very low temperatures also shows logarithmic decays.  This review gives a great discussion of this - I highly recommend it (even though the papers they cite from my PhD advisor's lab came after I left :-)  ).

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