Arcadian Functor

occasional meanderings in physics' brave new world

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Marni D. Sheppeard

Saturday, November 18, 2006


Back in the mid 1980s I was in the lab pounding the ingredients for a ceramic high Tc superconductor with a pestle and mortar. We would do this for a while with each sample to get the powder nice and homogeneous. In 1989 Fisher suggested the possibility of a new phase in superconductors, a disordered vortex-glass phase. Nowadays condensed matter physicists do all sorts of things with superconductors, such as construct precision clocks using niobium microwave cavities.

One of the most exciting developments in CMP at present is the theory of topological quantum computation. Particles with knotty statistics, called anyons, can be potentially used to build a fault tolerant quantum computer. And it also seems that materials science and nanotechnology is moving ahead in leaps and bounds.

Now imagine what we could do with a new physical theory, a theory that does not merely assume that the universe is FRW homogeneous and isotropic. After all, it's the matter that is interesting, not the inferred background in which it appears. Imagine a theory where anyon knots live instead in the pure world of categorical logic, where we are no longer constrained by the limitations of analytical geometry.


Blogger Mahndisa S. Rigmaiden said...

11 17 06

Well Miss Kea:
I am with you on considering the possibilities. I came across anyon physics some time ago when I was researching the Josephson effect and some Classical Chern Simon theory. See my riddle for a good hoot. As to the assumption of homogeneity and isotropy, well that one just seems naive...

November 18, 2006 2:25 PM  
Blogger Kea said...

Hi Mahndisa

Yes, I was interested in CSFT when Witten wrote his great Jones polynomial paper in 1989. Category theory makes braiding structures much clearer. Nowadays, of course, lots of people are into this.

November 18, 2006 4:28 PM  
Blogger Mahndisa S. Rigmaiden said...

11 18 06

Yes, I have seen quite a few papers on category theory and the Jones paper. However, the field of Topological Computing seems fairly arcane, and there is much work to be done. I have been looking over a paper by Simon and Bonesteel et al on using only one mobile quasiparticle in a weaving fashion over n-1 strings in a lattice, versus using n particles and wrapping them around one another. This is supposed to greatly simplify TQC, but experimental results have yet to be obtained. It seems like there is a very rich intermarriage between category theory, topology and braid theory. I like this mixture very much and appreciate your referring me to the Friedmen articles.

Anyonic physics is very interesting too, with many applications to condensed matter physics etc. So thanks for the references.

November 19, 2006 11:51 AM  

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