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Are the critical exponents for Anderson localization due to disorder well understood?

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Abstract

Semiclassical theory has been used, with some success, to discuss Anderson localization due to disorder. Our attention is focused on the quantum–chemical network model via a Boltzmann–like equation, and García-García’s semiclassical approach, contacted with early work of Care and March on compensated semiconductor. This work is related with the recent semiclassical treatment on the effect of disorder on the nature of electron states in the quantum–chemical network model.

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References

  1. Mott N.F., Twose W.D.: Adv. Phys. 10, 107–163 (1961)

    Article  CAS  Google Scholar 

  2. Dancz J., Edwards S.F., March N.H.: J. Phys. C: Solid State Phys. 6, 873–879 (1973)

    Article  CAS  Google Scholar 

  3. March N.H., Angilella G.G.N.: J. Math. Chem. 46, 532–549 (2009)

    Article  CAS  Google Scholar 

  4. Wegner F.J.: Z. Phyz. B 25, 327–337 (1976)

    Article  Google Scholar 

  5. F.J. Wegner, in Localization Interactions and Transport Phenomena (Springer Series in Solid Stale Science 61), ed by B. Kramer, G. Bergmann, Y. Bruynseraede (Springer, Berlin, 1985)

  6. Vollhardt D., Wölfle P.: Phys. Rev. Lett. 48, 699–702 (1982)

    Article  Google Scholar 

  7. Wegner F.J.: Nucl. Phys. B 316, 663–678 (1989)

    Article  Google Scholar 

  8. Wegner F.J.: Z. Phys. B 78, 33–43 (1990)

    Article  Google Scholar 

  9. Zhang Z.D.: Phil. Mag. 87, 5309–5419 (2007)

    Article  CAS  Google Scholar 

  10. March N.H., Zhang Z.D.: J. Math. Chem. 47, 520–538 (2010)

    Article  CAS  Google Scholar 

  11. Ławrynowicz J., Marchiafava S., Niemczynowicz A.: Adv. Appl. Clifford Alg. 20, 733–743 (2010)

    Article  Google Scholar 

  12. J. Ławrynowicz, S. Marchiafava, M. Nowak-Keͅpczyk, Trends in Differential Geometry, Complex analysis and Mathemtical Physics, Proceedings of the 9th International Workshop on Complex Structures, Integrability and Vector Fields, Sofia, Bulgaria, 25–29 August, ed by K. Sekigawa, V.S. Gerdjikov and S. Dimiev (World Scientific, Singapore, 2008), pp. 156–166 doi:10.1142/9789814277723_0018

  13. March N.H., Zhang Z.D.: Phys. Lett. A 373, 2075–2076 (2009)

    Article  CAS  Google Scholar 

  14. MacKinnon A., Kramer B.: Phys. Rev. Lett 47, 1546–1549 (1981)

    Article  Google Scholar 

  15. MacKinnon A., Kramer B.: Z. Phys. B53, 1–13 (1983)

    Article  Google Scholar 

  16. MacKinnon A.: Z. Phys. B59, 385–390 (1985)

    Article  Google Scholar 

  17. Pichard J.L., Sarma G.: J. Phys. C: Solid State Phys. 14, L127–132 (1981)

    Article  CAS  Google Scholar 

  18. Pichard J.L., Sarma G.: J. Phys. C: Solid State Phys. 14, L617–L625 (1981)

    Article  CAS  Google Scholar 

  19. Chayes J.T., Chayes L., Fisher D.S., Spencer T.: Phys. Rev. Lett. 57, 2999–3002 (1986)

    Article  Google Scholar 

  20. Harris A.B.: J. Phys. C: Solid State Phys. 7, 1671–1692 (1974)

    Article  Google Scholar 

  21. Anderson P.W.: Phys. Rev. 109, 1492–1505 (1958)

    Article  CAS  Google Scholar 

  22. Paalanen M.A., Thomas G.A.: Helv. Phys. Acta 56, 27–34 (1983)

    CAS  Google Scholar 

  23. Katsumoto S., Komori F., Sano N., Kobayashi S.: J. Phys. Soc. Japan 56, 2259–2262 (1987)

    Article  CAS  Google Scholar 

  24. Thomas G.A., Ootuka Y., Katsumoto S., Kobayashi S., Sasaki W.: Phys. Rev. B 25, 4288–4290 (1982)

    Article  CAS  Google Scholar 

  25. Markoš P.: J. Phys. A33, L393–L398 (2000)

    Google Scholar 

  26. MacKinnon A.: J. Phys.: Condens. Matter 6, 2511–2518 (1994)

    Article  CAS  Google Scholar 

  27. Kramer B., MacKinnon A.: Rep. Prog. Phys. 56, 1469–1564 (1993)

    Article  CAS  Google Scholar 

  28. A.M. García-García, Phys. Rev. Lett. 100, 076404-1-4 (2008)

    Google Scholar 

  29. J. Wang, A.M. García-García, Phys. Rev. E 79, 036206-1-10 (2009)

    Google Scholar 

  30. Varga I., Hofstetter E., Pipek J.: Phys. Rev. Lett. 82, 4683–4686 (1999)

    Article  CAS  Google Scholar 

  31. Care C.M., March N.H.: J. Phys. C: Solid State Phys. 4, L372–L376 (1971)

    Article  CAS  Google Scholar 

  32. Care C.M., March N.H.: Adv. Phys. 24, 101–116 (1975)

    Article  Google Scholar 

  33. Lagendijk A., van Tiggelen B., Wiersma D.S.: Phys. Today 62, 24–29 (2009)

    Article  CAS  Google Scholar 

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Authors and Affiliations

  1. Shenyang National Laboratory for Materials Science, Institute of Metal Research and International Centre for Materials Physics, Chinese Academy of Sciences, 72 Wenhua Road, 110016, Shenyang, People’s Republic of China

    Z. D. Zhang

  2. Donostia International Physics Center (DIPC), Paseo Manuel de Lardizábal, No. 4, 20018, Donostia, San Sebastián, Spain

    N. H. March

  3. Department of Physics, University of Antwerp, Antwerp, Belgium

    N. H. March

  4. Oxford University, Oxford, England, UK

    N. H. March

Authors
  1. Z. D. Zhang
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  2. N. H. March
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Correspondence to Z. D. Zhang.

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Zhang, Z.D., March, N.H. Are the critical exponents for Anderson localization due to disorder well understood?. J Math Chem 49, 816–820 (2011). https://doi.org/10.1007/s10910-010-9778-z

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  • DOI: https://doi.org/10.1007/s10910-010-9778-z

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