| The low dimensional model and the strong correlated electron model have been one of the most significant area in the research of the condensed matter theory. Since the discovery of the pyroconductivity and the BEC quantum hall effect, these models attracts more and more physicists' attentions. As an important realization in strong correlated electron theory, Bariev model has been widely investigated for many years, and shed light on the theoretical research in condensed matter physics. Many excellent works in this direction, concerning its integrabihty, exact solution, boundary effect and thermodynamic properties, was made in order to understand the physical nature of the model itself. For all the reasons above, it should be a very meaningful work to research the physical properties of the Bariev model in some more deeper level. In this thesis, we will show some effort in this direction thoroughly. The main ideas of the paper consists of two aspects: first, the purpose that investigate the relation between two models is to open out the physical properties thoroughly. scend, because of the correlated function of the Bariev model is hard to calculate, so i hope this thesis has the elicitation for calculation of the correlated function.The research area of the applicant's master thesis include from the Bariev model to the coulomb fermi gas with interactionThe Bethe Ansatz equation act an significant role in the integrabihty system. The mostly task of this thesis is that introduce the suitable continuum limit in which case Bariev model wound evolve as coulomb Fermi gas with reciprocity, according to deeply analyse and research the Bethe Ansatz equation of Bariev model and coulomb Fermi gas with reciprocity. Two-and N-component Bariev model are the two section of the investigation in this thesis. According to the investigation of the two-component Bethe Ansatz equation, we introduce into the suitable parameters and then successful import the continuum limit, whereafter research the integrable equation, TBA equation and free energy in the continuum limit one by one, at last triumphant prove the correctness of the continuum limit. In succession we develop the conclusion which have been demonstrated in two-component case to the N-component case, and discuss the behavior of the N-component Bariev model's Bethe Ansatz equation in the continuum limit. Finally, this thesis gives the definitude relation that evolve from Bariev model to coulomb Fermi gas with reciprocity and demonstrates its' correctness via three aspects: integral equations,TBA equation and free energy. By discuss the N-component case, the absolute homology condition for evolvement is discovered in two-component case and N-component case and this conclusion demonstrates that the evolutive condition has widely applicability for Bariev model. |
