Geometric magnetism in massive chaotic billiards

Journal of Physics A: Mathematical and General

Volumn 30, Issue 8, 1997, Pages 2853-2861

  Berry, M V ^a   Sinclair, E C ^a  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031582162     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/30/8/027     Document Type: Article

References (26)

1. Arnold V I, Kozlov V V and Neishtadt A I 1988 Dynamical systems. III Mathematical aspects of classical and celestial mechanics (Berlin: Springer)
2. Avron J E, Herbst I W and Simon B 1978 Separation of centre of mass in homogeneous magnetic fields Ann. Phys., NY 114 431-51
3. Berglund N and Kunz H 1995 Integrability and erdodicity of classical billiards in magnetic fields J. Stat. Phys. 83 81-126
4. Berry M V 1984 Quantal phase factors accompanying adiabatic changes Proc. R. Soc. A 392 45-57
5. _ 1989 Geometric Phases in Physics ed A Shapere and F Wilczek (Singapore: World Scientific) pp 7-28
6. _ 1996 The Levitron™: an adiabatic trap for spins Proc. R. Soc. A 452 1207-20
7. Berry M V and Robbins J M 1993a Chaotic classical and half-classical adiabatic reactions: geometric magnetism and deterministic friction Proc. R. Soc. A 442 659-72
8. _ 1993b Classical geometric forces of reaction: an exactly solvable model Proc. R. Soc. A 442 641-58
9. Cottingham W N and Hassan N 1990 The Berry phase and the hydrogen molecular ion in an external magnetic field J. Phys. B: At. Mol. Opt. Phys. 23 323-7
10. Hannay J H 1985 Angle variable anholonomy in adiabatic excursion of an integrable Hamiltonian J. Phys. A: Math. Gen. 18 221-30
11. Jackiw R 1988 Comm. At. Mol. Phys. 21 71-82
12. Jarzynski C 1992 Diffusion equation for energy in ergodic adiabatic ensembles Phys. Rev. A 46 7498-509
13. _ 1993a Energy diffusion in a chaotic adiabatic billiard gas Phys. Rev. E 48 4340-50
14. _ 1993b Multiple-time-scale approach to ergodic adiabatic systems: another look Phys. Rev. Lett. 71 839-42
15. _ 1995 Thermalization of a Brownian particle via coupling to low-dimensional chaos Phys. Rev. Lett. 74 2937-40
16. Littlejohn R G and Weigert S 1993 Adiabatic motion of a neutral spinning particle in an inhomogeneous magnetic field Phys. Rev. A 48 924-40
17. Lochak P and Meunier C 1988 Multiphase averaging for classical systems (New York: Springer)
18. Mead C A and Truhlar D G 1979 On the determination of Born-Oppenheimer nuclear motion wave functions including complications due to conical intersections and identical nuclei J. Chem. Phys. 70 2284-96
19. Messiah A 1962 Quantum Mechanics (Amsterdam: North-Holland)
20. Robbins J M 1994 The geometric phase for chaotic unitary families J. Phys. A: Math. Gen. 27 1179-89
21. Robbins J M and Berry M V 1992 The geometric phase for chaotic systems Proc. R. Soc. A 436 631-61
22. Robnik M 1986 Nonlinear Phenomena and Chaos ed S Sarkar (Bristol: Adam Hilger) pp 303-30
23. Robnik M and Berry M V 1985 Classical billiards in magnetic fields J. Phys. A: Math. Gen. 18 1361-78
24. Shapere A and Wilczek F eds 1989 Geometric Phases in Physics (Singapore: World Scientific)
25. Wilkinson M 1990 Dissipation by identical oscillators J. Phys. A: Math. Gen. 23 3603-11
26. Yin L and Mead C A 1992 Magnetic screening of nuclei by electrons as manifestation of geometric vector potential Theor. Chim. Acta 82 397-406