Normal and Anomalous Averages for Systems with Bose-Einstein Condensate

TL;DR

This paper analyzes the behavior of normal and anomalous averages in Bose-Einstein condensate systems across different temperature regimes, highlighting their varying significance and impact on system properties.

Contribution

It provides a detailed comparison of normal and anomalous averages across temperature regions, emphasizing the importance of anomalous averages at low and intermediate temperatures.

Findings

Anomalous averages are much smaller than normal averages near the critical temperature.

At low temperatures, anomalous averages dominate over normal averages.

The behavior of averages varies significantly across three temperature regions.

Abstract

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.