Condensation in ideal Fermi gases

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I investigate the possibility of condensation in ideal Fermi systems of general single particle density of states. For this I calculate the probability wₙ₀ of having exactly N₀ particles in the condensate and analyze its maxima. The existence of such maxima at macroscopic values of N₀ indicates a condensate. An interesting situation occurs for example in 1D systems, where wₙ₀ may have two maxima. One is at N₀=0 and another one may exist at finite N₀ (for temperatures bellow a certain condensation temperature). This suggests the existence of a first order phase transition. % The calculation of wₙ₀ allows for the exploration of ensemble equivalence of Fermi systems from a new perspective.