中国物理B ›› 2007, Vol. 16 ›› Issue (10): 2855-2861.doi: 10.1088/1009-1963/16/10/005

• GENERAL • 上一篇    下一篇

The geometric phase of the quantum systems with slow but finite rate of the external time-dependent field

贾欣燕, 李卫东, 梁九卿   

  1. Institute of Theoretical Physics, College of Physics and Electronics Engineering, Shanxi University, Taiyuan 030006, China
  • 收稿日期:2006-12-31 修回日期:2007-04-25 出版日期:2007-10-08 发布日期:2007-10-08
  • 基金资助:
    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

The geometric phase of the quantum systems with slow but finite rate of the external time-dependent field

Jia Xin-Yan(贾欣燕), Li Wei-Dong(李卫东)†, and Liang Jiu-Qing(梁九卿)   

  1. Institute of Theoretical Physics, College of Physics and Electronics Engineering, Shanxi University, Taiyuan 030006, China
  • Received:2006-12-31 Revised:2007-04-25 Online:2007-10-08 Published:2007-10-08
  • Supported by:
    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

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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.

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.

Key words: geometric phase, time-dependent gauge transformation

中图分类号:  (Phases: geometric; dynamic or topological)

  • 03.65.Vf