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Confined System with 1/r 2 Exchange Interaction and Its Application to Resonances in Narrow Channels

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Correlation Effects in Low-Dimensional Electron Systems

Part of the book series: Springer Series in Solid-State Sciences ((SSSOL,volume 118))

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Abstract

An integrable model for SU(v) electrons with inverse-square interaction is studied for the system with harmonic confinement. We obtain exactly the ground-state wavefunction of Jastrow type and the excited-state wavefunctions out of Hermite polynomials. The corresponding energy spectrum is computed exactly. The results are then applied to single-electron charging phenomena in narrow channels of semiconductor nano-structures.

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References

  1. F. Calogero, J. Math. Phys. 10, 2197 (1969); ibid 12, 419 (1971).

    Google Scholar 

  2. B. Sutherland, J. Math. Phys. 12, 246 (1971); Phys. Rev. A 4, 2019 (1971); ibid. A 5, 1372 (1971).

    Google Scholar 

  3. F. D. M. Haldane, Phys. Rev. Lett. 60, 635 (1988); ibid. 66, 1529 (1991).

    Google Scholar 

  4. B. S. Shastry, Phys. Rev. Lett. 60, 639 (1988); ibid. 69, 164 (1992).

    Google Scholar 

  5. Y. Kuramoto and H. Yokoyama, Phys. Rev. Lett. 67, 1338 (1991).

    Article  ADS  Google Scholar 

  6. Z. N. C. Ha and F. D. M. Haldane, Phys. Rev. B 46, 9359 (1992).

    Article  ADS  Google Scholar 

  7. N. Kawakami, Phys. Rev. B 46, 1005, 3192 (1992); J. Phys. Soc. Jpn. 62, 2270 (1993).

    Google Scholar 

  8. A. P. Polychronakos, Phys. Rev. Lett. 69, 703 (1992); K. Hikami and M. Wadati, Phys. Lett. A 173, 263 (1993).

    Google Scholar 

  9. B. Sutherland and B. S. Shastry, Phys. Rev. Lett. 71, 5 (1993).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  10. S. B. Field, M. A. Kastner, U. Meirav, J. H. F. Scott-Thomas, D. A. Antoniadis, H. I. Smith, and S. J. Wind, Phys. Rev. B 42, 3523 (1990).

    Article  ADS  Google Scholar 

  11. S. Tewari, Phys. Rev. B 46, 7782 (1992).

    Article  ADS  Google Scholar 

  12. N. F. Johnson and M. C. Payne, Phys. Rev. Lett. 70, 1513 (1993); ibid. 70, 3523 (1993).

    Google Scholar 

  13. Note that the spectrum for the SU(v) spin chain has been studied numerically by H. Frahm, J. Phys. A 26, L473 (1993), under a specific condition for the positions of particles.

    Google Scholar 

  14. J. A. Minahan and A. P. Polychronakos, Phys. Lett. B 302, 265 (1993).

    Article  ADS  MathSciNet  Google Scholar 

  15. J. A. Minahan and A. P. Polychronakos, Phys. Lett. B 302, 265 (1993).

    Article  ADS  MathSciNet  Google Scholar 

  16. N. Kawakami, J. Phys. Soc. Jpn. 62, 4163 (1993).

    Article  Google Scholar 

  17. P. J. Gambardella, J. Math. Phys. 18, 1172 (1975).

    Article  ADS  MathSciNet  Google Scholar 

  18. L. Brink, T. H. Hansson, and M. A. Vasiliev, Phys. Lett. B 286, 109 (1992).

    Article  ADS  MathSciNet  Google Scholar 

  19. K. Vacek, A. Okiji, and N. Kawakami, to be published.

    Google Scholar 

  20. N. Kawakami, Kyoto preprint YITP/K-1013 (1993).

    Google Scholar 

  21. K. Vacek, A. Okiji, and N. Kawakami, J. Phys. Soc. Jpn. 62, 3818 (1993).

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Applied Physics, Osaka University, Suita, Osaka 565, Japan

    K. Vacek & A. Okiji

  2. Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606, Japan

    N. Kawakami

Authors
  1. K. Vacek
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  2. A. Okiji
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  3. N. Kawakami
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Editor information

Editors and Affiliations

  1. Department of Applied Physics, Osaka University, Suita, Osaka 565, Japan

    Ayao Okiji

  2. Yukawa Institute for Theoretical Physics, Kyoto University, Sakyo-ku, Kyoto 606, Japan

    Norio Kawakami

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© 1994 Springer-Verlag Berlin Heidelberg

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Vacek, K., Okiji, A., Kawakami, N. (1994). Confined System with 1/r 2 Exchange Interaction and Its Application to Resonances in Narrow Channels. In: Okiji, A., Kawakami, N. (eds) Correlation Effects in Low-Dimensional Electron Systems. Springer Series in Solid-State Sciences, vol 118. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-85129-2_5

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  • DOI: https://doi.org/10.1007/978-3-642-85129-2_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-85131-5

  • Online ISBN: 978-3-642-85129-2

  • eBook Packages: Springer Book Archive

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