Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Geometric phase memories

The moment of conception of the geometric phase can be pinpointed precisely, but related ideas had been formulated before, in various guises. Not less varied were the ramifications that became clear once the concept was identified formally.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Figure 1: A polarization bull's-eye singularity photographed in the sky above Bristol University.

References

  1. Berry, M. V. Proc. R. Soc. Lond. A 392, 45–57 (1984).

    Article  ADS  Google Scholar 

  2. Percival, I. C. J. Phys. B 6, L229–L232 (1973).

    Article  ADS  Google Scholar 

  3. Porter, C. E. Statistical Theories of Spectra: Fluctuations (Academic Press, 1965).

    Google Scholar 

  4. Von Neumann, J. & Wigner, E. Phys. Z. 30, 467–470 (1929).

    Google Scholar 

  5. Berry, M. V. Ann. Phys. 131, 163–216 (1981).

    Article  ADS  Google Scholar 

  6. Uhlenbeck, K. Am. J. Math. 98, 1059–1078 (1976).

    Article  Google Scholar 

  7. Longuet-Higgins, H. C., Öpik, U., Pryce, M. H. L. & Sack, R. A. Proc. R. Soc. Lond. A 244, 1–16 (1959).

    ADS  Google Scholar 

  8. Berry, M. V. & Wilkinson, M. Proc. R. Soc. Lond. A 392, 15–43 (1984).

    Article  ADS  Google Scholar 

  9. Mead, C. A. & Truhlar, D. G. J. Chem. Phys. 70, 2284–2296 (1979).

    Article  ADS  Google Scholar 

  10. Simon, B. Phys. Rev. Lett. 51, 2167–2170 (1983).

    Article  ADS  MathSciNet  Google Scholar 

  11. Thouless, D. J., Kohmoto, M., Nightingale, M. P. & den Nijs, M. Phys. Rev. Lett. 49, 405–409 (1982).

    Article  ADS  Google Scholar 

  12. Wilczek, F. & Zee, A. Phys. Rev. Lett. 52, 2111–2114 (1984).

    Article  ADS  MathSciNet  Google Scholar 

  13. Hannay, J. H. J. Phys. A 18, 221–230 (1985).

    Article  ADS  MathSciNet  Google Scholar 

  14. Berry, M. V. J. Phys. A 18, 15–27 (1985).

    Article  ADS  MathSciNet  Google Scholar 

  15. Aharonov, Y. & Anandan, J. Phys. Rev. Lett. 58, 1593–1596 (1987).

    Article  ADS  MathSciNet  Google Scholar 

  16. Garrison, J. C. & Wright, E. M. Phys. Lett. A 128, 177–181 (1988).

    Article  ADS  MathSciNet  Google Scholar 

  17. Kuratsuji, H. & Iida, S. Prog. Theo. Phys. 74, 439–445 (1985).

    Article  ADS  Google Scholar 

  18. Berry, M. V. in Geometric Phases in Physics (eds Shapere, A. & Wilczek, F.) 7–28 (World Scientific, 1989).

    Google Scholar 

  19. Berry, M. V. & Robbins, J. M. Proc. R. Soc. Lond. A 442, 641–658 (1993).

    Article  ADS  Google Scholar 

  20. Berry, M. V. & Shukla, P. J. Phys. A 43, 045102 (2010).

    Article  ADS  MathSciNet  Google Scholar 

  21. Ramaseshan, S. & Nityananda, R. Curr. Sci. India 55, 1225–1226 (1986).

    Google Scholar 

  22. Pancharatnam, S. Proc. Ind. Acad. Sci. A 44, 247–262 (1956).

    Article  MathSciNet  Google Scholar 

  23. Berry, M. V. J. Mod. Opt. 34, 1401–1407 (1987).

    Article  ADS  Google Scholar 

  24. Berry, M. V. Curr. Sci. India 67, 220–223 (1994).

    Google Scholar 

  25. Budden, K. G. & Smith, M. S. Proc. R. Soc. Lond. A 350, 27–46 (1976).

    Article  ADS  Google Scholar 

  26. Berry, M. V. Phys. Today 43, 34–40 (December 1990).

    Article  ADS  Google Scholar 

  27. Berry, M. V. Proc. R. Soc. Lond. A 414, 31–46 (1987).

    Article  ADS  Google Scholar 

  28. Berry, M. V. Proc. R. Soc. Lond. A 422, 7–21 (1989).

    Article  ADS  Google Scholar 

  29. Berry, M. V. Proc. R. Soc. Lond. A 429, 61–72 (1990).

    Article  ADS  Google Scholar 

  30. Dingle, R. B. Asymptotic Expansions: Their Derivation and Interpretation (Academic Press, 1973).

    MATH  Google Scholar 

  31. Berry, M. V. & Howls, C. J. Proc. R. Soc. Lond. A 434, 657–675 (1991).

    Article  ADS  Google Scholar 

  32. Berry, M. V. in Asymptotics Beyond All Orders (eds Segur, H. & Tanveer, S.) 1–14 (Plenum, 1992).

    Google Scholar 

  33. Berry, M. V. & Howls, C. J. Phys. World 6, 35–39 (June 1993).

    Article  Google Scholar 

  34. Berry, M. V. in Proc. 9th Int. Cong. Logic Method. Phil. Sci. (eds Prawitz, D., Skyrms, B. & Westerståhl, D.) 597–607 (Elsevier, 1994).

    Google Scholar 

  35. Berry, M. V. in Sir Charles Frank OBE FRS, An Eightieth Birthday Tribute (eds Chambers, R. G., Enderby, J. E., Keller, A., Lang, A. R. & Steeds, J. W.) 207–219 (Adam Hilger, 1991).

    Google Scholar 

  36. Frank, F. C. Phil. Mag. 42, 809–819 (1951).

    Article  Google Scholar 

  37. Frank, F. C. Farad. Sci. Disc. 25, 19–28 (1958).

    Article  Google Scholar 

  38. Aharonov, Y. & Bohm, D. Phys. Rev. 115, 485–491 (1959).

    Article  ADS  MathSciNet  Google Scholar 

  39. Chambers, R. G. Phys, Rev. Lett. 5, 3–5 (1960).

    Article  ADS  Google Scholar 

  40. Nye, J. F. & Berry, M. V. Proc. R. Soc. Lond. A 336, 165–190 (1974).

    Article  ADS  Google Scholar 

  41. Nye, J. F. & Hajnal, J. V. Proc. R. Soc. Lond. A 409, 21–36 (1987).

    Article  ADS  Google Scholar 

  42. Nye, J. F. Natural Focusing and Fine Structure of Light: Caustics and Wave Dislocations (Institute of Physics Publishing, 1999).

    MATH  Google Scholar 

  43. Shapere, A. & Wilczek, F. Geometric Phases in Physics (World Scientific, 1989).

    MATH  Google Scholar 

  44. Zwanziger, J. W., Koenig, M. & Pines, A. Adv. Chem. Phys. 41, 601–646 (1990).

    Google Scholar 

  45. Markovski, B. & Vinitsky, S. I. Topological Phases in Quantum Theory (World Scientific, 1989).

    Google Scholar 

  46. Bohm, A. The Geometric Phase in Quantum systems: Foundations, Mathematical Concepts, and Applications in Molecular and Condensed-Matter Physics (Springer, 2003).

    Book  Google Scholar 

  47. Li, H.-Z. Global Properties of Simple Quantum Systems – Berry's Phase and Others (Shanghai Scientific and Technical Publishers, 1998).

    Google Scholar 

  48. Chruscinski, D. & Jamiolkowski, A. Geometric Phases in Classical and Quantum Mechanics (Birkhäuser, 2004).

    Book  Google Scholar 

  49. Berry, M. V., Bhandari, R. & Klein, S. Eur. J. Phys. 20, 1–14 (1999).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Berry, M. Geometric phase memories. Nature Phys 6, 148–150 (2010). https://doi.org/10.1038/nphys1608

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphys1608

This article is cited by

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing