The Study On The Berry Phase Of Two-particle Coupling

Since Berry proposed the existence of geometric phase in the periodic adiabatic process of quantum Hamilton systems in 1984, the theory of geometric phase for has attracted enormous interests. Samuel extended the geometric phase to noncyclic and nonadiabatic evolutions. There has been many experimental trials and theoretical analysis on geometric phase in fields of nuclear physics, atomic and molecular field, quantum calculation, optics, condensed matter physics and canonical field scopes. The discovery of geometric phase inspires people to reconsider several fundamental physics problems. Deep insight of geometric phase is beneficial for deep understanding of quantum mechanics.In this thesis, we mainly focused on the geometric phase for the interaction of two particles. Firstly, we discussed the effect of anisotropic coupling on geometric phase of a system in a time-dependent magnetic field and obtained the approximate instantaneous eigenstate of the Hamiltonian using perturbation method based on which we obtained the geometic phase. Finally we obtained the geometric phase of the Hamiltonian by constructing a time-dependent operator of SO(5) group...