Skip to main content
SpringerLink
Log in

A monatomic chain with an impurity in mass and Hooke constant

  • Regular Article
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

A classical monatomic chain with an impurity in both mass and Hooke constant is studied by means of the recurrence relations method. The momentum autocorrelation function of the impurity is contributed by resonant poles and a branch cut. Though the model has two pairs of poles but only one pair is physical and contributes a cosine to the momentum autocorrelation function, whose frequency and amplitude are derived. The cut contribution is given by a convolution product of a sine and a sum of two Bessel functions of zeroth and second order. The memory function of the model is also derived which is contributed by a pair of poles and a branch cut. The former gives a cosine and the latter a convolution of a sine and a sum of two Bessel functions. The ergodicity of the momentum of the impurity is also discussed.

Graphical abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. E.W. Montroll, R.B. Potts, Phys. Rev. 100, 525 (1955)

    Article  ADS  MathSciNet  Google Scholar 

  2. P. Mazur, E.W. Montroll, R.P. Potts, J. Wash. Acad. Sci. 46, 2 (1956)

    Google Scholar 

  3. A.A. Maradudin, E.W. Montroll, G.H. Weiss, inTheory of Lattice Dynamics in the Harmonic Approximation (Academic, New York, 1963), p. 179

  4. P. Dean, J. Inst. Math. Appl. 3, 98 (1967)

    Article  Google Scholar 

  5. R.F. Fox, Phys. Rev. A 27, 3216 (1983)

    Article  ADS  MathSciNet  Google Scholar 

  6. A.S. Baker Jr., A.J. Sievers, Rev. Mod. Phys. 47, S1 (1975)

    Article  Google Scholar 

  7. M.H. Lee, Phys. Rev. Lett. 49, 1072 (1982)

    Article  ADS  MathSciNet  Google Scholar 

  8. M.H. Lee, J. Math. Phys. 24, 2512 (1983)

    Article  ADS  MathSciNet  Google Scholar 

  9. M.H. Lee, J. Hong, J. Florencio Jr., Phys. Scr. T19, 498 (1987)

    Article  ADS  Google Scholar 

  10. U. Balucani, M.H. Lee, V. Tognetti, Phys. Rep. 373, 409 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  11. M.H. Lee, J. Hong, Phys. Rev. Lett. 48, 634 (1982)

    Article  ADS  Google Scholar 

  12. M.H. Lee, J. Hong, Phys. Rev. B 32, 7734 (1985)

    Article  ADS  Google Scholar 

  13. E.M. Silva, Phys. Rev. E 92, 042146 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  14. S. Sen, M. Long, Phys. Rev. B 46, 14617 (1992)

    Article  ADS  Google Scholar 

  15. S. Sen, Physica A 360, 304 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  16. A.V. Mokshin, R.M. Yulmetyev, P. Hanggi, Phys. Rev. Lett. 95, 200601 (2005)

    Article  ADS  Google Scholar 

  17. S.X. Chen, Y.Y. Shen, X.M. Kong, Phys. Rev. B 82, 174404 (2010)

    Article  ADS  Google Scholar 

  18. O.F. de Alcantara Bonfim, J. Florencio, Phys. Rev. E 92, 042115 (2015)

    MathSciNet  Google Scholar 

  19. M.E.S. Nunes, E.M. Silva, P.H.I. Martins, J.A. Plascak, J. Florencio, Phys. Rev. E 98, 042124 (2018)

    Article  ADS  Google Scholar 

  20. J. Florencio, Jr. M.H. Lee, Phys. Rev. A 31, 3231 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  21. A. Wierling, Eur. Phys. J. B 85, 20 (2012)

    Article  ADS  Google Scholar 

  22. M.H. Lee, J. Florencio Jr., J. Hong, J. Phys. A 22, L331 (1989)

    Article  ADS  Google Scholar 

  23. M.B. Yu, Eur. Phys. J. B 86, 57 (2013)

    Article  ADS  Google Scholar 

  24. M.B. Yu, Phys. Lett. A 380, 3583 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  25. M.B. Yu, Eur. Phys. J. B 90, 87 (2017)

    Article  ADS  Google Scholar 

  26. M.B. Yu, Physica A 398, 252 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  27. M.B. Yu, Eur. Phys. J. B 91, 25 (2018)

    Article  ADS  Google Scholar 

  28. G.E. Roberts, H. Kaufman, inTable of Laplace Transforms (Saunders, Philadelphia, 1966), p. 196

  29. I.S. Gradsgteyn, I.N. Ryzhik, inTable of Integrals, Series and Products, 7th edn. (A&P 2007), p. 1111

  30. I.S. Gradsgteyn, I.N. Ryzhik, inTable of Integrals, Series and Products, 7th edn. (A&P 2007), p. 398

  31. P. Ullersma, Physica 32, 27 (1966)

    Article  ADS  MathSciNet  Google Scholar 

  32. P. Ullersma, Physica 32, 56 (1966)

    Article  ADS  MathSciNet  Google Scholar 

  33. P. Ullersma, Physica 32, 74 (1966)

    Article  ADS  MathSciNet  Google Scholar 

  34. S. Sen, Z.X. Cai, S.D. Mahanti, Phys. Rev. Lett. 72, 3287 (1994)

    Article  ADS  Google Scholar 

  35. M.H. Lee, Phys. Rev. Lett. 87, 250061 (2001)

    Google Scholar 

  36. M.H. Lee, Phys. Rev. Lett. 98, 190601 (2007)

    Article  ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. 8000 Badura Ave., 1053, Las Vegas, Nevada, 89113, USA

    Ming B. Yu

Authors
  1. Ming B. Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ming B. Yu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yu, M.B. A monatomic chain with an impurity in mass and Hooke constant. Eur. Phys. J. B 92, 272 (2019). https://doi.org/10.1140/epjb/e2019-100383-1

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/e2019-100383-1

Keywords

Search

Navigation