几何相位

在物理学中,几何相位是一种经典力学量子力学相位完整群、或威尔森回卷,来自哈密尔顿算符绝热过程绝热定理英语Adiabatic Theorem)。[1]

印度物理家S. Pancharatnam英语S. Pancharatnam(盘查拉特纳姆,1956年)发现了几何相位,[2][3] 后来迈克尔·贝里再发现了(1984年)。[4]

几何相位的其他名字包括Pancharatnam相位贝里相位

几何相位例子包括阿哈罗诺夫–波姆效应潜在能量的表面[5]经典力学傅科摆[6]

度量量子力学的几何相位需要干涉实验

量子力学的相位编辑

若系统处于第n个量子态,则通过哈密尔顿绝热过程(或路径积分表述):

 

其中的  是贝里相位,也可能写为

 

所以贝里相位是贝里曲率的积分。R是参数,  是参数空间的回卷。

应用编辑

参见编辑

脚注编辑

  1. ^ Solem, J. C.; Biedenharn, L. C. Understanding geometrical phases in quantum mechanics: An elementary example. Foundations of Physics. 1993, 23 (2): 185–195. Bibcode:1993FoPh...23..185S. doi:10.1007/BF01883623. 
  2. ^ S. Pancharatnam. Generalized Theory of Interference, and Its Applications. Part I. Coherent Pencils. Proc. Indian Acad. Sci. A. 1956, 44 (5): 247–262. doi:10.1007/BF03046050. 
  3. ^ H. C. Longuet Higgins; U. Öpik; M. H. L. Pryce; R. A. Sack. Studies of the Jahn-Teller effect .II. The dynamical problem. Proc. R. Soc. A. 1958, 244 (1236): 1–16. Bibcode:1958RSPSA.244....1L. doi:10.1098/rspa.1958.0022. See page 12
  4. ^ M. V. Berry. Quantal Phase Factors Accompanying Adiabatic Changes. Proceedings of the Royal Society A. 1984, 392 (1802): 45–57. Bibcode:1984RSPSA.392...45B. doi:10.1098/rspa.1984.0023. 
  5. ^ G. Herzberg; H. C. Longuet-Higgins. Intersection of potential energy surfaces in polyatomic molecules. Discuss. Faraday Soc. 1963, 35: 77–82. doi:10.1039/DF9633500077. 
  6. ^ Wilczek, F.; Shapere, A. (编). Geometric Phases in Physics. Singapore: World Scientific. 1989: 4. 
  7. ^ Wilczek, F.; Shapere, A. (编). Geometric Phases in Physics. Singapore: World Scientific. 1989: 4. 
  8. ^ Jens von Bergmann; HsingChi von Bergmann. Foucault pendulum through basic geometry. Am. J. Phys. 2007, 75 (10): 888–892. Bibcode:2007AmJPh..75..888V. doi:10.1119/1.2757623. 
  9. ^ C.Z.Ning and H. Haken. Geometrical phase and amplitude accumulations in dissipative systems with cyclic attractors. Phys. Rev. Lett. 1992, 68 (14): 2109–2122. Bibcode:1992PhRvL..68.2109N. PMID 10045311. doi:10.1103/PhysRevLett.68.2109. 
  10. ^ C.Z.Ning and H. Haken. The geometric phase in nonlinear dissipative systems. Mod. Phys. Lett. B. 1992, 6 (25): 1541–1568. Bibcode:1992MPLB....6.1541N. doi:10.1142/S0217984992001265.