Broken symmetry, rigidity, and dissipative structures

On monday I am giving the opening talk at the Australasian Workshop on Emergent Quantum Matter. Since it is a broad audience with a range of backgrounds I am going to give a tutorial talk, building on the UQ colloquium I gave earlier this year.  Later I will post my draft slides.

One concept I want to expand on is the concept of rigidity, associated with broken symmetry. To do this I am reading a nice article "Some general thoughts about broken symmetry," written by Phil Anderson in 1981. It is reprinted in A Career in Theoretical Physics, and here is a scanned copy of the article. It contains the figure above.

What is the connection between the "rigidity" of  solids and broken symmetry? A liquid is invariant under continuous translations and rotations. When it becomes a solid it is only invariant under discrete rotations and translations. Symmetry is broken. Unlike a liquid, a solid can "sustain/resist" a shear stress. Solids are rigid.

I also want to say something about non-equilibrium. Anderson has something critical to say about "dissipative structures" such as Bernard cells associated with self-organisation and hydrodynamic instabilities.