Abstract 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.
Received: 31 December 2006
Revised: 25 April 2007
Accepted manuscript online:
PACS:
03.65.Vf
(Phases: geometric; dynamic or topological)
Fund: 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), the Natural
Science Foundation of Shanxi Province (Grant No~200
Cite this article:
Jia Xin-Yan(贾欣燕), Li Wei-Dong(李卫东), and Liang Jiu-Qing(梁九卿) The geometric phase of the quantum systems with slow but finite rate of the external time-dependent field 2007 Chinese Physics 16 2855
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