Normal and Anomalous Averages for Systems with Bose-Einstein Condensate
  The comparative behaviour of normal and anomalous averages as functions of momentum or energy, at different temperatures, is analysed for systems with Bose-Einstein condensate. Three qualitatively distinct temperature regions are revealed: The critical region, where the absolute value of the anomalous average, for the main energy range, is much smaller than the normal average. The region of intermediate temperatures, where the absolute values of the anomalous and normal averages are of the same order. And the region of low temperatures, where the absolute value of the anomalous average, for practically all energies, becomes much larger than the normal average. This shows the importance of the anomalous averages for the intermediate and, especially, for low temperatures, where these anomalous averages cannot be neglected. 
V.I. Yukalov and E.P. Yukalova