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In this talk I will first review some interesting physics of ultra-cold fermions. This includes how to tune the interactions via a Feshbach resonance and BCS-Bose Einstein condensation (BEC) crossover of fermionic superfluids. Then I will show that directly applying BCS wavefunction or linear response theory can lead to incorrect results. Two examples, the structure factor and the compressibility, will be explicitly evaluated and demonstrate such pitfalls in BCS theory and its extension to the crossover. Host: Lijun Zhu, lijun@lanl.gov |