摘要
With the help of the time-dependent gauge transformation technique, we have studied the geometric phase of a spin-half particle in a rotating magnetic field. We have found that the slow but finite frequency of the rotating magnetic field will make the difference between the adiabatic geometric phase and the exact geometric phase. When the frequency is much smaller than the energy space and the adiabatic condition is perfectly guaranteed, the adiabatic approximation geometric phase is exactly consistent with the adiabatic geometric phase. A simple relation for the accuracy of the adiabatic approximation is given in terms of the changing rate of the frequency of the rotating magnetic field and the energy level space.
With the help of the time-dependent gauge transformation technique, we have studied the geometric phase of a spin-half particle in a rotating magnetic field. We have found that the slow but finite frequency of the rotating magnetic field will make the difference between the adiabatic geometric phase and the exact geometric phase. When the frequency is much smaller than the energy space and the adiabatic condition is perfectly guaranteed, the adiabatic approximation geometric phase is exactly consistent with the adiabatic geometric phase. A simple relation for the accuracy of the adiabatic approximation is given in terms of the changing rate of the frequency of the rotating magnetic field and the energy level space.
基金
Project supported by the State Key Development Program for Basic Research of China （Grant No 2006CB921603）, the National Natural Science Foundation of China （Grant Nos 10444002 and 10674087）7 the Natural Science Foundation of Shanxi Province （Grant No 2006011004）7 the Shanxi Provincial Foundation for Returned Scholars the Scientific Research Foundation of the State Human Resource Ministry for Returned Chinese Scholars, and the Scientific Research Foundation for the Returned 0verseas Chinese Scholars, Ministry of Education of China.
