Arnab Ghosh, Sudarson Sekhar Sinha, Deb Shankar Ray
We examine the weakly interacting atoms in an ultracold Fermi gas leading to Fermi condensation, from a theoretical perspective. It has been shown that Fermi condensate can be described as a fermionic coherent state, a state of macroscopic occupation of a single quantum state. These coherent states are the eigenstates of fermionic annihilation operators, the eigenvalues being anti-commuting numbers or Grassmann numbers. By exploiting the simple rules of Grassmann algebra and a close kinship between relations evaluated for more familiar bosonic fields and those for fermionic fields, we derive the thermodynamic limit, the spontaneous symmetry breaking and the excitation spectrum of the fermionic system.
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http://arxiv.org/abs/1301.4079
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