几何相位

在经典力学及量子力学中，几何相位是当系统经历了周期性绝热过程的一个周期后获得的相位差。这种相位差是由哈密顿量的参数空间的集合性质导致的。[1]

印度物理家Shivaramakrishnan Pancharatnam（英语：Shivaramakrishnan Pancharatnam）（盘查拉特纳姆，1956年）与 H.C.Longuet-Higgins （1958）分别独立的在经典光学领域和分子物理领域发现了几何相位，[2][3] 迈克尔·贝里推广了这一现象（1984年）。[4]

几何相位的其他名字包括Pancharatnam相位或贝里相位。

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]和经典力学的傅科摆。[6]

度量量子力学的几何相位需要干涉的实验。

量子力学的相位

若系统处于第n个量子态，则通过哈密尔顿的绝热过程（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

参见

脚注

  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. ^ 6.0 6.1 Wilczek, F.; Shapere, A. (编). Geometric Phases in Physics. Singapore: World Scientific. 1989: 4. 
  7. ^ 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. 
  8. ^ 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. 
  9. ^ 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. 

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