Fluctuations of the Fermi condensate in ideal gases

TL;DR

This paper analyzes the fluctuations of the fermionic condensate and particles above it in ideal gases, comparing canonical and grandcanonical ensembles, and finds their fluctuations are largely consistent across ensembles.

Contribution

It provides a detailed numerical and analytical comparison of fermionic condensate fluctuations in different statistical ensembles for systems with constant density of states.

Findings

Condensate fluctuations are similar in canonical and grandcanonical ensembles.

Number of particles above the condensate is insensitive to ensemble choice.

Small corrections arise from total particle number fluctuations in the grandcanonical ensemble.

Abstract

We calculate numerically and analytically the fluctuations of the fermionic condensate and of the number of particles above the condensate for systems of constant density of states. We compare the canonical fluctuations, obtained from the equivalent Bose condensate fluctuation, with the grandcanonical fermionic calculation. The fluctuations of the condensate are almost the same in the two ensembles, with a small correction comming from the total particle number fluctuation in the grandcanonical ensemble. On the other hand the number of particles above the condensate and its fluctuation is insensitive to the choice of ensemble.