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Geometric phase from a combined evolution‐operator‐invariant technique

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Abstract

The quantum phase problem is investigated by a synthesis of the evolution operator technique and method of invariants. This approach has been found to be quite effective to disclose interrelationship between geometric phases differing in the nature of evolution and to obtain results for them without invoking the concept of parallel transport in the projective Hilbert space. The usefulness of the method developed is ascertained by studying the geometric phases associated with spinor evolutions in rotating magnetic field.

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References

  1. Y. Aharonov and J. Anandan, Phys. Rev. Lett. 58 (1987) 1593.

    Article  Google Scholar 

  2. J. Anandan, Phys. Lett. A129 (1988) 201.

    Google Scholar 

  3. V.I. Arnold, Mathematical Methods of Classical Mechanics (Springer-Verlag, New York, 1978) chapter 10.

    Google Scholar 

  4. M.V. Berry, Proc. Roy. Soc. London A392 (1984) 45.

    Google Scholar 

  5. T. Bitter and D. Dubbers, Phys. Rev. Lett. 59 (1987) 251.

    Article  CAS  Google Scholar 

  6. A. Bohm, Quantum Mechanics, Foundations and Applications, 3rd ed. (Springer-Verlag, New York, 1993) chapter 22.

    Google Scholar 

  7. A. Bohm, B. Kendrick and M.E. Loewe, Int. J. Quantum Chem. 41 (1992) 53.

    Article  Google Scholar 

  8. J.M. Cerveró and J.D. Lajarreta, J. Phys. A: Math. Gen. 22 (1989) L663.

    Article  Google Scholar 

  9. J.M. Cerveró and J.D. Lajarreta, Phys. Lett. A156 (1991) 201.

    Google Scholar 

  10. C.M. Cheng and P.C.W. Fung, J. Phys. A: Math. Gen. 22 (1989) 3493.

    Article  Google Scholar 

  11. H. Goldstein, Classical Mechanics, 2nd ed. (Narosa Pub. House, New Delhi, 1985) chapter 11.

    Google Scholar 

  12. G. Herzberg and H.C. Longuet-Higgins, Disc. Faraday Soc. 35 (1963) 77.

    Article  Google Scholar 

  13. H.C. Longuet-Higgins, Proc. Roy. Soc. London A344 (1975) 147.

    Google Scholar 

  14. B. Kendrick and R.T. Pack, J. Chem. Phys. 102 (1995) 1994.

    Article  CAS  Google Scholar 

  15. H. Kozumi and S. Sugano, J. Chem. Phys. 101 (1994) 4903.

    Article  Google Scholar 

  16. A. Kuppermann and Y.S.M. Wu, Chem. Phys. Lett. 205 (1993) 577.

    Article  CAS  Google Scholar 

  17. O. Kwon, C. Ahn and Y. Kim, Phys. Rev. A46 (1992) 5354.

    Google Scholar 

  18. L.D. Landau and E.M. Lifshitz, Mechanics, 3rd ed. (Pergamon Press, New York, 1982) chapter 7.

    Google Scholar 

  19. H.R. Lewis, Jr., and W.B. Riesenfeld, J. Math. Phys. 10 (1969) 1458.

    Article  Google Scholar 

  20. C.A. Mead, Chem. Phys. 49 (1980) 23, 33.

    Article  CAS  Google Scholar 

  21. C.A. Mead, Rev. Mod. Phys. 64 (1992) 51.

    Article  CAS  Google Scholar 

  22. C. Mead and D. Truhlar, J. Chem. Phys. 70 (1979) 2284.

    Article  CAS  Google Scholar 

  23. S.S. Mizrahi, Phys. Lett. A138 (1989) 465.

    Google Scholar 

  24. N. Mukunda and R. Simon, Ann. Phys. 228 (1993) 205.

    Article  Google Scholar 

  25. D. Neuhauser, R.S. Judson, D.J. Kouri, D.E. Adelman, N.E. Shafer, D.A.V. Kliner and R.N. Zare, Science 257 (1992) 519.

    CAS  Google Scholar 

  26. G. Ni, S. Chen and Y. Shen, Phys. Lett. A197 (1995) 100.

    Google Scholar 

  27. S. Pancharatnam, Proc. Ind. Acad. Sci. A44 (1956) 247.

    Google Scholar 

  28. D.J. Richardson, A.I. Kilvington, K. Green and S.K. Lamoreaux, Phys. Rev. Lett. 61 (1987) 2030.

    Article  Google Scholar 

  29. J.J. Sakurai, Modern Quantum Mechanics (Addison-Wesley, New York, 1985) chapter 5.

    Google Scholar 

  30. J. Samuel and R. Bhandari, Phys. Rev. Lett. 60 (1988) 2339.

    Article  Google Scholar 

  31. A.N. Seleznyova, Phys. Rev. A51 (1995) 950.

    Google Scholar 

  32. B. Simon, Phys. Rev. Lett. 51 (1983) 2167.

    Article  Google Scholar 

  33. E.C.G. Sudarsan, J. Anandan and T.R. Govindarajan, Phys. Lett. A164 (1992) 133.

    Google Scholar 

  34. A.G. Wagh and V.C. Rakhecha, Phys. Lett. A190 (1992) 71.

    Google Scholar 

  35. Y.S.M. Wu and A. Kuppermann, Chem. Phys. Lett. 201 (1993) 178.

    Article  CAS  Google Scholar 

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Panja, M., Talukdar, B. Geometric phase from a combined evolution‐operator‐invariant technique. Journal of Mathematical Chemistry 21, 183–192 (1997). https://doi.org/10.1023/A:1019170302545

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