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Multi-particle and multi-state Landau-Zener model: Dynamic matrix approach

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Abstract.

The paper presents the multi-particle and multi-state Landau-Zener problem and focuses on indistinguishable particles with degenerate states applying the Dynamics matrix approach. It is observed that the probabilities are described by the Binomial law with the limiting values that achieved exact results for spin \( S=1/2\) and \( S=1\) Landau-Zener problems. The derivation of the generalized multi-particle probability function is observed to be equivalent to solving a Landau-Zener problem for particle number equal to twice the spin.

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References

  1. M.V. Volkov, V.N. Ostrovsky, J. Phys.: At. Mol. Opt. Phys. B 638, 90 (2005)

    Google Scholar 

  2. N.A. Sinitsyn, Generalizations of the Landau-Zener theory in the physics of nanoscale systems (Texas University Press, New York, 2004)

  3. Michael F. O'Keeffe, Eugene M. Chudnovsky, Dmitry A. Garanin, Phys. Rev. B 87, 174418 (2013)

    Article  ADS  Google Scholar 

  4. M. LaHaye, J. Suh, P. Echternach, K. Schwab, M. Roukes, Nature 459, 960 (2009)

    Article  ADS  Google Scholar 

  5. D.A. Harmin, P.N. Price, Phys. Rev. A 49, 1933 (1994)

    Article  ADS  Google Scholar 

  6. V.A. Yurovsky, A. Ben-Reuven, P.S. Julienne, Phys. Rev. A 65, 043607 (2002)

    Article  ADS  Google Scholar 

  7. Yu. Gefen, E. Ben-Jacob, A.O. Caldeira, Phys. Rev. B 36, 2770 (1987)

    Article  ADS  Google Scholar 

  8. D. Iliescu, S. Fishman, E. Ben-Jacob, Phys. Rev. B 46, 675 (1992)

    Article  Google Scholar 

  9. N.A. Sinitsy, Phys. Rev. B 66, 205303 (2002)

    Article  ADS  Google Scholar 

  10. G. Dattoli, J. Gallardo, A. Torre, Phys. Rev. B 27, 772 (1986)

    MathSciNet  Google Scholar 

  11. C. Itzykson, J.B. Zuber, Quantum Field Theory (McGraw-Hill Press, New York, 1980)

  12. Jean-Louis Loday, Frédéric Chapoton, Alesandra Frabelti, François Goichot, Dialgebras and related operads, in Lecture Notes in Mathematics, Vol. 1763 (Springer, 2001)

  13. L.D. Landau, Phys. Z. Sowjetunion 2, 46 (1932)

    Google Scholar 

  14. C. Zener, Proc. R. Soc. London A 137, 720 (1932)

    Article  Google Scholar 

  15. E. Majorana, Nuovo Cimento 83, 013609 (1932)

    Google Scholar 

  16. E.C.G. Stückelberg, Helv. Phys. Acta 9, 50 (1932)

    Google Scholar 

  17. H.B. Heersche et al., Phys. Rev. Lett. 96, 206801 (2006)

    Article  ADS  Google Scholar 

  18. L. Bogani, W. Wernsdorfer, Nat. Mater 7, 179 (2008)

    Article  ADS  Google Scholar 

  19. V.L. Pokrovsky, N.A. Sinitsyn, Phys. Rev. B 69, 104414 (2004)

    Article  ADS  Google Scholar 

  20. A.K. Kazansky, V.N. Ostrovsky, J. Phys. At. Mol. Opt. Phys. B 29, 855 (1996)

    Article  ADS  Google Scholar 

  21. A. Aguilar, M. Gonzalez, L.V. Poluyanov, J. Phys. At. Mol. Opt. Phys. B 33, 4815 (2000)

    Article  ADS  Google Scholar 

  22. K.-A. Suominen, E. Tiesinga, P.S. Julienne, Phys. Rev. A 58, 3983 (1998)

    Article  ADS  Google Scholar 

  23. M.B. Kenmoe, H.N. Phien, M.N. Kiselev, L.C. Fai, Phys. Rev. B 87, 224301 (2013)

    Article  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. Mesoscopic and Multilayer Structures Laboratory, Department of Physics, Faculty of Science, University of Dschang, Cameroon, P.O.Box: 479, Dschang, Cameroon

    L. C. Fai, M. Tchoffo & M. N. Jipdi

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  1. L. C. Fai
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  2. M. Tchoffo
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  3. M. N. Jipdi
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Correspondence to M. N. Jipdi.

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Fai, L.C., Tchoffo, M. & Jipdi, M.N. Multi-particle and multi-state Landau-Zener model: Dynamic matrix approach. Eur. Phys. J. Plus 130, 71 (2015). https://doi.org/10.1140/epjp/i2015-15071-y

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  • DOI: https://doi.org/10.1140/epjp/i2015-15071-y

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