Monomer And The Geometric Phase Of A Many-body Quantum System

This thesis concentrates on the issues of the geometric phase of composite system: the dependence of geometric phase on the coupling between the two subsystems, the effect of the entanglement among particles on the geometric phase of the composite system, the influence of symmetry of Hamilton of composite system on the geometric phase, and the complexity of geometric phase of multi-particle system. Using algebraic dynamics, the geometric phase of Landau system with a rotating magnetic field is studied numerically, and the great difference between adiabatic geometric phase and non-adiabatic geometric phase is shown: in non-adiabatic evolution, non-adiabatic quantum effect results in the non-periodicity and the complexity of geometric phase, which reflected the influence of environment on the system. The investigation of the geometric phase of a 3 spin-1/2 chain shows that the symmetry of Hamilton affects the structure of geometric phase: when the symmetry of Hamilton is broken, a drastic change in the structure of the geometric phase takes place. The fractal phenomenon of geometric phase in an entangled multi-particle system is also explored, and the box-counting dimensions of the fractal-like curves of the evolution of geometric phases are calculated. The results of the thesis are helpful to extend the understanding of geometric phase.