Regime of Validity of the Pairing Hamiltonian in the Study of Fermi Gases

Details Regime of Validity of the Pairing Hamiltonian in the Study of Fermi Gases Regime of Validity of the Pairing Hamiltonian in the Study of Fermi Gases

2006-03-12

arxiv.org/abs/physics/0603093v1

Phys. Rev. B, 73, 212502 (2006)

Physics

Atomic Physics

2 figures, 1 table

Scientific paper

10.1103/PhysRevB.73.212502

The ground state energy and pairing gap of the interacting Fermi gases calculated by the {\it ab initio} stochastic method are compared with those estimated from the Bardeen-Cooper-Schrieffer pairing Hamiltonian. We discuss the ingredients of this Hamiltonian in various regimes of interaction strength. In the weakly interacting ($1/ak_F <<0$) regime the BCS Hamiltonian should describe Landau quasi-particle energies and interactions, on the other hand in the strongly pairing regime, that is $1/ak_F \gtrsim 0$, it becomes part of the bare Hamiltonian. However, the bare BCS Hamiltonian is not adequate for describing atomic gases in the regime of weak to moderate interaction strength $-\infty < 1/ak_F <0$ such as $ak_F \sim -1$. PACS: 05.30.Fk, 03.75.Ss, 21.65.+f

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