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Berry Phase and its Unitarily Invariant Generalization

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Condensed Matter Theories

Part of the book series: Condensed Matter Theories ((COMT,volume 7))

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Abstract

The geometrical phase in quantum mechanics discovered by Berry is not invariant under unitary transformations. It is generalized to be unitarily invariant and applicable to nonadiabatic and noncyclic systems. Examples of a spin-1/2 particle in a precessing magnetic field and a time-dependent generalized harmonic oscillator are considered.

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References

  1. M. V. Berry, Proc. R. Soc. A 392:45 (1984).

    Article  ADS  MATH  Google Scholar 

  2. J. W. Zwanziger, M. Koenig, and A. Pines, Annu. Rev. Phys. Chem. 41:601 (1990).

    Article  ADS  Google Scholar 

  3. J. Hannay, J. Phys. A 18:221 (1985).

    Article  MathSciNet  ADS  Google Scholar 

  4. M. V. Berry, J. Phys. A 18:15 (1985).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. G. Giavarini, E. Gozzi, D. Rohrlich, and W. D. Thacker, Phys. Lett. A 137:235 (1989); J. Phys. A 22:3513 (1989).

    Google Scholar 

  6. D. H. Kobe, J. Phys. A 23:4249 (1990).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. K.-H Yang, Ann. Phys. (N.Y.) 101:62 (1976).

    Article  ADS  Google Scholar 

  8. D. H. Kobe, V. C. Aguilera-Navarro, S. M. Kurcbart, and A. H. Zimerman, Phys. Rev. A 42:3744 (1990).

    Article  MathSciNet  ADS  Google Scholar 

  9. X. Gao, J. B. Xu, and T. Z. Qian, Ann. Phys. (N.Y.) 204:235 (1990).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. R. Jackiw, Int. J. Mod. Phys. A 3:285 (1988).

    Article  MathSciNet  ADS  Google Scholar 

  11. P. de S. Gerbert, Ann. Phys. (N.Y.) 189:155 (1989).

    Article  ADS  Google Scholar 

  12. D. H. Kobe, J. Phys. A 24:2763 (1991).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. L. I. Schiff, “Quantum Mechanics,” McGraw-Hill, New York (1968), 3rd ed., pp. 289–291.

    Google Scholar 

  14. D. H. Kobe and K.-H. Yang, Eur. J. Phys. 8:236 (1987).

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Physics, University of North Texas, Denton, Texas, 76203-5368, USA

    Donald H. Kobe

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  1. Donald H. Kobe
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Editor information

Editors and Affiliations

  1. University of Buenos Aires, Vicente López, Argentina

    Araceli Noemi Proto  & Jorge Luis Aliaga  & 

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© 1992 Springer Science+Business Media New York

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Kobe, D.H. (1992). Berry Phase and its Unitarily Invariant Generalization. In: Proto, A.N., Aliaga, J.L. (eds) Condensed Matter Theories. Condensed Matter Theories, vol 7. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-3352-8_4

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  • DOI: https://doi.org/10.1007/978-1-4615-3352-8_4

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-6478-8

  • Online ISBN: 978-1-4615-3352-8

  • eBook Packages: Springer Book Archive

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