Or, why bother with 1D physics?
The attentive reader will have already spotted a problem here: isn't the world 3D? Well of course it is, but nevertheless there are basically two compelling reasons why 1D systems have something to tell us about the world.
- -Such things actually exist!
- It's not hard to find everyday examples which are best thought of as problems in fewer dimensions than 3. Ordinary water waves may be thought of as a 2D problem if we can ignore any compression of the fluid (for water, this works rather well). If you are unable to squash the fluid, all you can really do is move the surface, reducing the problem to one in 2D. A common example of an essentially 1D phenomenon is traffic jams, although condensed matter physicists tend to study rather more esoteric examples such as edge waves in the quantum hall effect.
- -We have a better toolkit to use on 1D systems.
- Over the years, people have been able to come up with very clever tricks for solving problems in 1D. These tricks don't work in the messy world where things can move around anywhere, but in 1D allow us to get a handle on strongly interacting systems, something well out of reach in higher dimensions.
I teach Mathematical Methods to first year NatScis at Emma and have also supervised Ben Simons' Part III course on Quantum Condensed Matter Field Theory.
Summer Schools and Conferences
I was lucky enough to attend the fantastic Boulder Summer School 2013 on Disorder and Dynamics in Quantum Systems. In July 2014 I was at the ICTP in Trieste for the school on Non-linear Dynamics, Dynamical Transitions and Instabilities.