Research on the Thermodynamic Property of Weakly Interacting Fermi Gases Through N-E-V Distribution and Pseudopotential Method

Abstract

As the experiments of quantum system are conducted in the external field where the volume, energy and particle number are variable, the thermodynamic property of weakly interacting Fermi system is studied in this paper through the statistical distribution (N-E-V distribution) of a completely open system where the volume, energy and particle number are variable. Firstly, analytical expressions of internal energy, the equation of state, entropy and heat capacity expressed by Fermi integral are worked out. On that basis, the analytical expression and results of numerical calculation of the above thermodynamic quantities in extremely low temperature conditions can be known. Then, comparison between the calculations of N-E-V distribution and pseudopotential method (the volume and particle number remain the same) is drawn. The results show that the calculation of N-E-V distribution always makes up for the deviation of that of pseudopotential method. Besides, the most special thing about the calculation derived from N-E-V distribution is that the temperature variation curve of internal energy and that in the ideal Fermi system intersect. The characteristics of energy transfer between "attractive force" and "repulsive force" at the intersection temperature t c , which indicates that there is a phase transition. The intersection temperature does not change with the scattering length a (a<0 attractive force, a>0 repulsive force). Moreover, the intersection temperature of all weakly interacting Fermi system is 0.184 times as large as Fermi temperature, which is within the range of temperature for BEC and BCS phase transition and BEC-BCS crossover.