Application Of Flow Equation Method In "Two Band" BCS Superconductor

The flow equation method, which was proposed by Wegner F. J. Wilson K. and S.D. Glazek, is the application and development of renormalization group approach. The main idea of this method is that by means of a series of infinitesimal continuous unitary transformation, the Hamiltonian of the system is turned to a diagonalization or local diagonalization.This method possesses an important advantage with the selectivity of generating function, which is widely used in condensed matter physics and high energy physics.In this paper, the flow equation method is used to study the electrical properties of the "two band" BCS superconducting model by using Wegner flow operator function. The energy spectrum, energy gap and the electron occupation in the two bands are shown through calculation. It is reconfirmed that the method of flow equation is of significance in the research of condensed matter physics. In the first chapter, the superconductor is briefly introduced, including its history and development, its properties of superconducting and applications are shown. In the second chapter, the introduction of the flow equation is concisely described, and the theoretical ideas and characteristics of the flow equation method are introduced in detail.In the meanwhile the average of the physical operator is given. In the third chapter, the method of flow equation is used to study Fermi pair model. Using Wegner flow generating function operator selection method, the flow parameters /approach infinity, the Hamiltonian system can be diagonalization, and the energy spectrum of the system is obtained. Under the same unitary transformation, the system of the related physical quantity can be transform, meet with Hamiltonian system same flow equation, the system energy gap can be obtained. In the fourth chapter, the "two band" BCS superconducting model is studied by using the flow equation method. The Hamiltonian operator and the variation of electronic operator under unitary transformation are obtained by adopting the method of Wegner operator generating function. In the l approach infinity, the Hamiltonian of the diagonal form is given, thus the energy spectrum, the energy gap and the number of electrons in the two energy band are obtained, which depend on the temperature.