Discover
/
Article

Anticipations of the Geometric Phase

DEC 01, 1990
The notion that a quantum system’s wovefunction may not return to its original phase after its parameters cycle slowly around a circuit had many precursors—in polarized light, radio waves, molecules, matrices and curved surfaces.

DOI: 10.1063/1.881219

Michael Berry

In science we like to emphasize the novelty and originality of our ideas. This is harmless enough, provided it does not blind us to the fact that concepts rarely arise out of nowhere. There is always a historical context, in which isolated precursors of the idea have already appeared. What we call “discovery” sometimes looks, in retrospect, more like emergence into the air from subterranean intellectual currents.

This article is only available in PDF format

References

  1. 1. M. V. Berry, Proc. R. Soc. London, Ser. A 392, 45 (1984);
    reprinted in ref. 2, p.124.

  2. 2. A. Shapere, F. Wilczek, eds., Geometric Phases in Physics, World Scientific, Singapore (1989).

  3. 3. R. Jackiw, Commun. At. Mol. Phys. 21, 71 (1988).
    J. W. Zwanziger, M. Koenig, A. Pines, Annu. Rev. Phys. Chem. (1990), in press.

  4. 4. B. Markovski, V. I. Vinitsky, Topological Phases in Quantum Theory, World Scientific, Singapore (1989).

  5. 5. M. V. Berry, in Anomalies, Phases, Defects, M. Bregola, G. Marmo, G. Morandi, eds., Bibliopolis, Naples (1990), p. 125.

  6. 6. S. M. Rytov, Dokl. Akad. Nauk. USSR 18, 263 (1938);
    reprinted in ref. 4, p. 6.
    V. V. Vladimirskii, Dokl. Akad. Nauk. USSR 21, 222 (1941);
    reprinted in ref. 4, p. 11.

  7. 7. M. V. Berry, Nature 326, 277 (1987); https://doi.org/NATUAS
    reprinted in ref. 2, p. 197.

  8. 8. M. V. Berry, in Fundamental Aspects of Quantum Theory, NATO Adv. Stud. Inst. Ser., vol. 144, V. Gorini, A. Frigerio, eds., Plenum, New York (1986), p. 267.

  9. 9. S. Pancharatnam, Proc. Ind. Acad. Sci. A 44, 247 (1956);
    reprinted in ref. 2, p. 51.S. Ramaseshan, R. Nityananda, Curr. Sci. (India) 55, 1225 (1986).

  10. 10. M. V. Berry, J. Mod. Opt. 34, 1401 (1987); https://doi.org/JMOPEW
    reprinted in ref. 2, p. 67.

  11. 11. M. S. Smith, Proc. R. Soc. London, Ser. A 346, 59 (1975).
    K. G. Budden, M. S. Smith, Proc. R. Soc. London, Ser. A 350, 27 (1975).

  12. 12. M. V. Berry, Proc. R. Soc. London (1990), in press.

  13. 13. H. C. Longuet‐Higgins, U. Öpik, M. H. L. Pryce, R. A. Sack, Proc. R. Soc. London, Ser. A 244, 1 (1958).

  14. 14. G. Herzberg, H. C. Longuet‐Higgins, Faraday Soc. Disc. 35, 77 (1963);
    reprinted in ref. 2, p. 74.

  15. 15. G. Delacrétaz, E. R. Grant, R. L. Whetten, L. Wöste, J. W. Zwanziger, Phys. Rev. Lett. 56, 2598 (1986); https://doi.org/PRLTAO
    reprinted in ref. 2, p. 240.

  16. 16. V. I. Arnold, Mathematical Methods of Classical Dynamics, Springer‐Verlag, New York (1978).

  17. 17. K. Uhlenbeck, Am. J. Math. 98, 1059 (1976).https://doi.org/AJMAAN

  18. 18. G. Darboux, Lecons sur la Théorie Générale des Surfaces, vol. 4, Gauthier‐Villars, Paris (1896), note VII, p. 448.

  19. 19. M. V. Berry, J. H. Hannay, J. Phys. A 10, 1809 (1977).https://doi.org/JPHAC5

  20. 20. F. C. Frank, Faraday Soc. Disc. 25, 19 (1958).

  21. 21. M. V. Berry, in Sir Charles Frank 80th Birthday Festschrift, R. G. Chambers, J. E. Enderby, A. Keller, A. R. Lang, J. W. Steeds, eds., Adam Hilger, Bristol (1990), in press.

  22. 22. A. J. Stone, Proc. R. Soc. London, Ser. A 351, 141 (1976);
    reprinted in ref. 2, p. 80.

  23. 23. C. A. Mead, D. G. Truhlar, J. Chem. Phys. 70, 2284 (1979); https://doi.org/JCPSA6
    reprinted in ref. 2, p. 90.

  24. 24. M. V. Berry in reference 2, p. 26.

More about the Authors

Michael Berry. University of Bristol, Bristol, England.

Related content
/
Article
Although motivated by the fundamental exploration of the weirdness of the quantum world, the prizewinning experiments have led to a promising branch of quantum computing technology.
/
Article
As conventional lithium-ion battery technology approaches its theoretical limits, researchers are studying alternative architectures with solid electrolytes.
/
Article
Bottom-up self-assembly is a powerful approach to engineering at small scales. Special strategies are needed to formulate components that assemble into predetermined shapes with precise sizes.
/
Article
The polymath scientist leaves behind a monumental legacy in both the scientific and political realms.
This Content Appeared In
pt-cover_1990_12.jpeg

Volume 43, Number 12

Get PT in your inbox

Physics Today - The Week in Physics

The Week in Physics" is likely a reference to the regular updates or summaries of new physics research, such as those found in publications like Physics Today from AIP Publishing or on news aggregators like Phys.org.

Physics Today - Table of Contents
Physics Today - Whitepapers & Webinars
By signing up you agree to allow AIP to send you email newsletters. You further agree to our privacy policy and terms of service.