Theoretical and Mathematical Physics

, Volume 181, Issue 2, pp 1396–1404 | Cite as

Correlated Lloyd model: Exact solution

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Abstract

We describe an exactly solvable model of a disordered system that is a generalized Lloyd model; it differs from the classical model because the random potential is not a δ-correlated random process. We show that the exact average Green’s function in this case is independent of the correlation radius of the random potential and, as in the classical Lloyd model, is a crystal Green’s function whose energy argument acquires an imaginary part dependent on the disorder degree.

Keywords

Lloyd model exactly solvable model correlated disordered system density of states average Green’s function 

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References

  1. 1.
    F. M. Izrailev, A. A. Krokhin, and N. M. Makarov, Phys. Rep., 512, 125–254 (2012); arXiv:1110.1762v1 [cond-mat.dis-nn] (2011).ADSCrossRefMathSciNetGoogle Scholar
  2. 2.
    M. Titov and H. Schomerus, Phys. Rev. Lett., 95, 126602 (2005).ADSCrossRefGoogle Scholar
  3. 3.
    L. I. Deych, M. V. Erementchouk, and A. A. Lisyansky, Phys. B, 338, 79–81 (2003).ADSCrossRefGoogle Scholar
  4. 4.
    A. Croy, P. Cain, and M. Schreiber, Eur. Phys. J. B, 82, 107–112 (2011).ADSCrossRefMathSciNetGoogle Scholar
  5. 5.
    O. Derzhko and J. Richter, Phys. Rev. B, 59, 100–103 (1999).ADSCrossRefGoogle Scholar
  6. 6.
    O. Derzhko and J. Richter, Phys. Rev. B, 55, 14298–14310 (1997).ADSCrossRefGoogle Scholar
  7. 7.
    V. A. Malyshev, A. Rodriguez, and F. Dominguez-Adame, Phys. Rev. B, 60, 14140–14146 (1999).ADSCrossRefGoogle Scholar
  8. 8.
    F. A. B. F. de Moura and M. L. Lyra, Phys. Rev. Lett., 81, 3735–3738 (1998).ADSCrossRefGoogle Scholar
  9. 9.
    D. H. Danlap, H.-L. Wu, and P. W. Phillips, Phys. Rev. Lett., 65, 88–91 (1990).ADSCrossRefGoogle Scholar
  10. 10.
    G. G. Kozlov, Theor. Math. Phys., 171, 531–540 (2012).CrossRefMATHGoogle Scholar
  11. 11.
    G. G. Kozlov, Appl. Math., 2, 965–974 (2011).CrossRefGoogle Scholar
  12. 12.
    F. J. Dyson, Phys. Rev., 92, 1331–1338 (1953).ADSCrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    P. Lloyd, J. Phys. C, 2, 1717–1725 (1969).ADSCrossRefGoogle Scholar
  14. 14.
    C. R. Gochanour, H. C. Andersen, and M. D. Fayer, J. Chem. Phys., 70, 4254–4271 (1979).ADSCrossRefGoogle Scholar
  15. 15.
    G. G. Kozlov, “The watching operators method in the theory of Frenkel exciton: Novel criterion of localization and its exact calculation for the non diagonal disordered 1D chain’s zero-state,” arXiv:cond-mat/9909335v1 (1999).Google Scholar
  16. 16.
    I. M. Lifshits, S. A. Gredeskul, and L. A. Pastur, Introduction to the Theory of Disordered Systems [in Russian], Nauka, Moscow (1982); English transl., Wiley-Interscience, New York (1988).Google Scholar
  17. 17.
    B. M. Miller and A. R. Pankov, Theory of Stochastic Processes in Examples and Problems [in Russian], Fizmatlit, Moscow (2007).MATHGoogle Scholar
  18. 18.
    E. S. Ventsel’ and L. A. Ovcharov, Theory of Random Processes and Its Engineering Application [in Russian], Vyshaya Shkola, Moscow (2000).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  1. 1.Fock Institute of PhysicsSt. Petersburg State UniversitySt. PetersburgRussia

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