GEOMETRIC PHASES IN PHYSICS

Transcription

1 Advanced Series in Mathematical Physics. Vol. 5 GEOMETRIC PHASES IN PHYSICS UNiVEKSH&TSBBUOTHEK HANNOVER TECWNiSCHE INFORMAT1ONSBI8UOTHEK Alfred Shapere Frank Wilczek World Scientific Singapore New Jersey London Hong Kong

2 XI CONTENTS Preface A Reader's Guide v vii Chapter 1 INTRODUCTION AND OVERVIEW 3 [1.1] M. V. Berry, "The Quantum Phase, Five Years After"* 7 [1.2] R. Jackiw, "Three Elaborations on Berry's Connection, Curvature and Phase," Int. J. Mod. Phys. A3 (1988) Chapter 2 ANTICIPATIONS 45 [2.1 ] S. Pancharatnam, "Generalized Theory of Interference, and its Applications," from Collected Works of S. Pancharatnam (Oxford University Press, UK, 1975) 51 [2.2] M. V. Berry, "The Adiabatic Phase and Pancharatnam's Phase for Polarized Light,"/ Mod. Optics 34 (1987) [2.3] G. Herzberg and H. C. Longuet-Higgins, "Intersection of Potential Energy Surfaces in Polyatomic Molecules," Disc. Farad. Soc. 35 (1963) [2.4] A. J. Stone, "Spin-Orbit Coupling and the Intersection of Potential Energy Surfaces in Polyatomic Molecules," Proc. R. Soc. Lond. A351 (1976) [2.5] C. A. Mead and D. G. Truhlar, "On the Determination of Bom-Oppenheimer Nuclear Motion Wave Functions Including Complications due to Conical Intersections and Identical Nuclei,"/. Chem. Phys. 70 (05) (1979) [2.6] Y. Aharonov and D. Bohm, "Significance of Electromagnetic Potentials in the Quantum Theory," Phys. Rev. 115 (19S9) Chapter 3 FOUNDATIONS 113 [3.1] M. V. Berry, "Quantal Phase Factors Accompanying Adiabatic Changes," Aw. R. Lond. A392 (1984)

3 Xll [3.2] B. Simon, "Holonomy, the Quantum Adiabatic Theorem, and Berry's Phase,"Phys. Rev. Lett. 51 (1983) [3.3] F. Wilczek and A. Zee, "Appearance of Gauge Structure in Simple Dynamical Systems," Phys. Rev. Lett. 52 (1984) [3.4] Y. Aharonov and J. Anandan, "Phase Change during a Cyclic Quantum Evolution," Phys. Rev. Lett. 58 (1987) [3.5] J. Samuel and R. Bhandari, "General Setting for Berry's Phase," Phys. Rev. Lett. 60 (1988) [3.6] H. Kuratsuji and S. Iida, "Effective Action for Adiabatic Process," Prog. Theo. Phys. 74 (1985) [3.7] J. Moody, A. Shapere and F. Wilczek, "Adiabatic Effective Lagrangians"* * 160 Chapter 4 SOME APPLICATIONS AND TESTS 187 [4.1] A. Tomita and R. Chiao, "Observation of Berry's Topological Phase by Use of an Optical Fiber," Phys. Rev. Lett. 57 (1986) [4.2] M. V. Berry, "Interpreting the Anholonomy of Coiled Light,"Nature 326 (1987) [4.3] J. Moody, A. Shapere and F. Wilczek, "Realizations of Magnetic-Monopole Gauge Fields: Diatoms and Spin Precession,"Phys. Rev. Lett. 56 (1986) [4.4] D. Suter, G. C. Chingas, R. A. Harris and A. Pines, "Berry's Phase in Magnetic Resonance,"Mo/. Phys. 61 (1987) [4.5] R. Tycko, "Adiabatic Rotational Splittings and Berry's Phase in Nuclear Quadrupole Resonance," Phys. Rev. Lett. 58 (1987) [4.6] D. Suter, K. T. Mueller and A. Pines, "Study of the Aharonov-Anandan Quantum Phase by NMR Interferometry," Phys. Rev. Lett. 60 (1988) [4.7] A. Zee, "Non-Abelian Gauge Structure in Nuclear Quadrupole Resonance," Phys. Rev. A38 (1988) [4.8] C. A. Mead, "Molecular Kramers Degeneracy and Non-Abelian Adiabatic Phase Factors," Phys. Rev. Lett. 59 (1987) [4.9] B. Zygelman, "Appearance of Gauge Potentials in Atomic Collision Physics,"Ws. Lett. A125 (1987)

4 xin [4.10] G. Delacretaz, E. R. Grant, R. L. Whetten, L. Woste and J. W. Zwanziger, "Fractional Quantization of Molecular Pseudorotation in N& 3,"Phys. Rev. Lett. 56 (1986) Chapter 5 FRACTIONAL STATISTICS 247 [5.1] F. Wilczek and A. Zee, "Linking Numbers, Spin, and Statistics of Solitons,"i%ys. Rev. Lett. 51 (1983) [5.2] Y. S. Wu, "Multiparticle Quantum Mechanics Obeying Fractional Statistics," fvys. Rev. Lett. 53 (1984) [5.3] D. P. Arovas, R. Schrieffer, F. Wilczek and A. Zee, "Statistical Mechanics of Anyom " Nucl. Phys. B251 (1985) Chapter 6 THE QUANTIZED HALL EFFECT 273 [6.1] D. Arovas, J. R. Schrieffer and F. Wilczek, "Fractional Statistics and the Quantum Hall Effect," Phys. Rev. Lett. 53 (1984) [6.2] D. P. Arovas, "Topics in Fractional Statistics"* 284 [6.3] S. M. Girvin and A. H. MacDonald, "Off-Diagonal Long-Range Order, Oblique Confinement, and the Fractional Quantum Hall Effect,"Phys. Rev. Lett 58 (1987) [6.4] J. E. Avron, A. Raveh and B. Zur, "Quantum Conductance in Networks,"Phys. Rev. Lett. 58 (1987) [6.5] R. B. Laughlin, "Superconducting Ground State of Noninteracting Particles Obeying Fractional Statistics," Phys. Rev. Lett. 60(1988) [6.6] M. Wilkinson, "An Example of Phase Holonomy in WKB Theory,"/ Phys. A17 (1984) Chapter 7 WESS-ZUMINO TERMS AND ANOMALIES 355 [7.1] M. Stone, "Born-Oppenheimer Approximation and the Origin of Wess-Zumino Terms: Some Quantum-Mechanical Examples," Phys. Rev. D33 (1986) [7.2] J. Goldstone and F. Wilczek, "Fractional Quantum Numbers on Solitons," Phys. Rev. Lett. 47 (1981) [7.3] E. Witten, "Global Aspects of Current Algebra," Nucl. Phys. B223 (1983) 422 '> 369 \

5 7.4] I. J. R. Aitchison, "Berry Phases, Magnetic Monopoles, and Wess-Zumino Terms or How the Skyrmion got its Spin," Acta Phys. Polonica B18 (1987) ' [7.5] P, Nelson and L. Alvarez-Gaume, "Hamiltonian Interpretation of Anomalies," Commun. Math. Phys. 99 (1985) Chapter 8 CLASSICAL SYSTEMS 423 [8.1] J. H. Hannay, "Angle Variable Holonomy in Adiabatic Excursion of an Integrable Hamiltonian,"/ Phys. A18 (1985) [8.2] M. V. Berry, "Classical Adiabatic Angles and Quantal Adiabatic Phase,"/ Phys. A18 (1985) [8.3] A. Shapere and F. Wilczek, "Gauge Kinematics of Deformable Bodies," to appear in A. J. Phys 449 [8.4] A. Shapere and F. Wilczek, "Geometry of Self-Propulsion at Low Reynolds Number,"/ FluidMech. 198 (1989) Chapter 9 ASYMPTOTICS 493 [9.1] M. V. Berry, "Quantum Phase Corrections From Adiabatic Iteration," Proc. R. Soc. Lond. A414 (1987)