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Universal upper bound for the tunneling rate of a large quantum spin

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Abstract

An upper bound is derived for the tunneling rate of a spin with large spin quantum numberS. The bound isuniversal in the sense that it does not depend on the specific form of the anisotropy (i.e., the potential barrier). The method of proof relies on the exponential localization theorem of Fröhlich and Lieb and lends precise support to a rather suggestive interpretation put forth in a WKB analysis of van Hemmen and Sütő. The resulting bound agrees with their expression for the tunneling rate in the limit of largeS.

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References

  1. Leggett, A. J., Chakravarty, S., Dorsey, A. T., Fisher, M. P. A., Garg, A., Zwerger, W.: Rev. Mod. Phys.59, 1 (1987)

    Google Scholar 

  2. Vourdas, A., Bishop, R. F.: J. Phys.G11, 95 (1985)

    Google Scholar 

  3. van Hemmen, J. L., Sütő, A.: Europhys. Lett.1, 481 (1986)

    Google Scholar 

  4. van Hemmen, J. L., Sütő, A.: Physica141B, 37 (1986)

    Google Scholar 

  5. Enz, M., Schilling, R.: J. Phys.C19, 1765 (1986)

    Google Scholar 

  6. Scharf, G., Wreszinski, W. F., van Hemmen, J. L.: J. Phys.A20, 4309 (1987)

    Google Scholar 

  7. van Hemmen, J. L., Sütő, A.: Z. Phys.B61, 263 (1985)

    Google Scholar 

  8. Chudnowsky, E. M., Gunther, L.: Quantum tunneling of magnetization in small ferromagnetic particles, Phys. Rev. Lett.60, 661 (1988)

    Google Scholar 

  9. Kirsch, W., Simon, B.: Universal lower bounds on eigenvalue splittings for one-dimensional Schrödinger operators. Commun. Math. Phys.97, 453 (1985), and references therein

    Google Scholar 

  10. Fröhlich, J., Lieb, E. H.: Phase transitions in anisotropic lattice spin systems. Commun. Math. Phys.60, 233 (1978)

    Google Scholar 

  11. Kato, T.: Perturbation theory for linear operators. Berlin, Heidelberg, New York: Springer Verlag 1966, Chap II

    Google Scholar 

  12. Brink, D. M., Satchler, G. R.: Angular momentum, 2nd ed. Oxford: Oxford University Press 1968, Eqs. (2.15), (2.17), and (2.18)

    Google Scholar 

  13. Harrell, E. M.: Double wells. Commun. Math. Phys.75, 239 (1980)

    Google Scholar 

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Author notes

  1. W. F. Wreszinski

    Present address: Instituto de Física, Universidade de São Paulo, Caixa Postal 20516, 01498, São Paulo, Brazil

Authors and Affiliations

  1. Universität Heidelberg, Sonderforschungsbereich 123, D-6900, Heidelberg, Federal of Republic of Germany

    J. L. van Hemmen & W. F. Wreszinski

Authors
  1. J. L. van Hemmen
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  2. W. F. Wreszinski
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Additional information

Communicated by B. Simon

Supported in part by the Conselho Nacional de Desenvolvimento Cientifico e Technológico (CNPq)

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van Hemmen, J.L., Wreszinski, W.F. Universal upper bound for the tunneling rate of a large quantum spin. Commun.Math. Phys. 119, 213–219 (1988). https://doi.org/10.1007/BF01217739

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  • DOI: https://doi.org/10.1007/BF01217739

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