First-order coherence in an atomic condensate at finite temperature

The field fluctuations of a Bose-Einstein condensate can be studied in terms of the first-order correlation function, which obeys a Yukawa-like equation already introduced in a previous work and expressed here in a real and complex notation. When the equation is reformulated using the number-conserving Bogoliubov approximation, it yields results that present quantitative differences with respect to the standard symmetry-breaking approach. Finally, we introduce an approximation to evaluate the correlation function for sufficiently high temperatures.