Investigation Of Thermodynamic Properties Of Weakly Interacting Fermi System By The N-E-V Distribution

With the development of cooling and atom-trapping technology the experiments and theories on the nature of the bose system and Fermi system have aroused people’s great interest, so have the Bose-Einstein condensation of Fermi molecules formed at low temperature and superflow phenomenon of Fermi atoms. Considering that the relevant experiment of quantum system (Fermi system or bose system) is conducted in a magnetic trap or light trap. So the volume, particle number and energy of the system are variable. However, the conventional methods of statistical physics, such as microcanonical ensemble, canonical ensemble and grand canonical ensemble, their volume is constant. Therefore, the thermodynamical property of Fermi system at low temperature is studied by using the statistical distribution (N-E-V distribution) of completely open system with variable particles number, volume and energy, which is more practical than that by a pseudopotential method based on canonical distribution. In this thesis, based on the pseudopotential method, the statistical distribution of completely open system we get the thermodynamical function of Fermi gases with weak interaction, the main contents are arranged as follow:In Chapter 1, the quantum statistics, Fermi condensation and related experimental techniques, the research status and significance of Fermi gas have been introduced briefly. In Chapter 2, the thermodynamic properties of weakly interacting Fermi systems are studied by applying the distribution of N-E-V. The analytical expressions of internal energy, equation of state, entropy, heat capacity of Fermi system with weak interaction are figured out. The calculation results at low temperature are compared with the calculated results of canonical distribution. In Chapter 3, considering that most relevant experiments of Femi system are conducted under the constrain of variable external field of volume, energy and particle number, the magnetic field is applied to adjust the scattering length among atoms in the Feshbach resonance-existing system. In terms of this fact, the thermodynamic properties of weakly interacting Fermi gases in weak magnetic field are studied by means of the N-E-V distribution. Based on the Chapter 2, Chapter 4 combing with the local-density approximation, the thermodynamic properties of weakly interacting Fermi systems are studied under the condition of strong magnetic in the unidimentional limited external potential like V(r)=-By field. The analytical expressions of chemical potential, internal energy and heat capacity are calculated with Fermi integral form. On the basis of it, the analytical expressions of chemical potential, internal energy and numerical results are calculated under extreme conditions of low temperature. The calculation results of the thesis are compared to that by using the canonical distribution.Finally, the whole thesis is summarized and the prospect of future study in the field is put forward.