Abstract
We studied the possibility of a crossover from the BCS theory to a Bose-Einstein condensation (BEC) for a non-Fermi system using the field theoretical method. We use as a description for the non-Fermi system the model proposed by Anderson, based on an anomalous Green function of the form G( k , ω) = g(α)ω c α /[iω − ϵ( k )] 1−α . We showed that this crossover is possible as a function of the interaction strength: the weak coupling limit can be described by the BCS theory and the strong coupling limit by the Bose-Einstein condensation of a preformed pairs gas. Using numerical methods we showed that the crossover is smooth, varying continuously as a function of the interaction constant. A more interesting result is the fact that the same crossover can be discussed in terms of the non-Fermi Anderson constant α.
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