Quantum Matter Lecture 8

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okay welcome back feel a little bit frazzled today I spent the morning reading to my daughter I read is your mama a llama to her 40 times in a row this is really great literature if you if you happen to be four months old highly recommended anyways whatever it kept her from crying and that was what kept her from crying so is your mama a llama it is okay sorry that digression decide today we going to study Ginsberg Landau theory for people who studied lambda theory of phase transitions and Ginsburg lambda theory before this will look a little bit familiar but then we will extend onward to see the relationship to the Andersen Higgs mechanism application to superconductors and we use Ginsburg Lando theory to derive some interesting results about superconductors which maybe even those people who study phase transitions might not have seen before so to start our exploration into Ginsberg Landau Fieri we going to start with the simple case of a neutral superfluid neutral superfluid and we write down the Ginsberg Landau free energy GL free energy which is exactly the form energy which is exactly the form of the gross pitaevskii