Generalized Bose-Einstein Condensation and BCS-Bose Crossover Theory

We show how critical temperatures Tc from the BCS-Bose crossover theory (defined self-consistently by both the gap and fermion-number equations) requires unphysically large couplings for the Cooper/BCS model interaction to differ significantly from the Tc of ordinary BCS theory (where the number equation is replaced by the assumption that the chemical potential equals the Fermi energy). Furthermore, within a recent generalization of Bose-Einstein condensation (GBEC) that includes electron and also, without loss of generality, hole Cooper pairs (CPs), both species interacting with unpaired electrons and holes, it is shown that although explicitly ignoring either holeor electron CPs yields the precise BCS gap equation for all temperatures T , only half of the T = 0 BCS rigorous-upper-bound condensation energy is obtained. PACS # 74.20.-z; 74.20.Mn; 05.30.Fk; 05.30.Jp