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What is so amazing about the degeneracy pressure for Fermi liquids?
I just finished preparing my undergraduate lecture on ideal Fermi gases at zero temperature. Here are my slides. (Note. The derivations ar...
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This week Nobel Prizes will be announced. I have not done predictions since 2020 . This is a fun exercise. It is also good to reflect on w... -
The Ising model is a paradigm in both statistical mechanics and condensed matter physics. Today for most theorists it is so familiar that so... -
Some of my colleagues and I have started an interesting discussion about how to teach quantum theory to undergraduates. We have courses in t...
Just to verify that I understand (roughly) the origin of the "rigidity" of the order parameter… In the "mexican hat" picture, where the symmetry is broken by a free energy that goes as power 2n>2 in the (complex) order parameter, the order parameter for the ground state moves off the top of the hat and into the brim. Out on the brim, the powers 4 and over will begin to dominate the free energy, leading to a greater second derivative at the ground state, hence more "rigidity" in the modulus of the order parameter. Is this a good way to understand?
ReplyDeleteNo. This is not what the rigidity is about.
DeleteThe rigidity refers to spatial variations of the order parameter. The Mexican hat has many degenerate minima. At any one point in space the order parameter may have one of these values. I can have a slow spatial variation of the order parameter across the system. The rigidity refers to the total energy cost associated with these slow spatial variations.