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Lecture on Debye model for solids
I just finished preparing my undergraduate lecture on the Debye model for solids. Here are my slides . The course is a third-year course on...
I just finished preparing my undergraduate lecture on the Debye model for solids. Here are my slides . The course is a third-year course on...
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.