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An Evaluation of Collective Mode in Weak and Strong Coupling Limit of One-Dimensional Fermi Gas

Shreemant Raman and L. K. Mishra

In this paper, we have studied the one-dimensional Fermi gas with attractive δ interaction potential in the quasi-particle random phase approximation at zero temperature. Using the theoretical formalism of Alm and Schuck, we have studied the behavior of collective modes over the whole coupling regime from weak coupling (high density) to strong coupling (low density). We observe that in the weakcoupling limit particle-hole RPA is approached to low momenta and the collective mode in the strong coupling limit reproduces the Bogoliubov mode for the weakly interacting bosons.