Skip to main content
Log in

Longitudinal permittivity of a quantum degenerate collisional plasma

  • Published:
Theoretical and Mathematical Physics Aims and scope Submit manuscript

Abstract

We find the permittivity of a degenerate electron gas for a collisional plasma. We use the Wigner-Vlasov-Boltzmann kinetic equation with the collision integral in the relaxation form in the coordinate space. We study the Kohn permittivity singularities and reveal their spreading in the collisionless plasma.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. P. K. Shukla and B. Eliasson, Phys. Usp., 53, 51–76 (2010).

    Article  ADS  Google Scholar 

  2. B. Eliasson and P. K. Shukla, J. Plasma Phys., 76, 7–17 (2010); arXiv:0911.4594v1 [physics.plasm-ph] (2009).

    Article  ADS  Google Scholar 

  3. V. P. Silin and A. A. Ruhadze, Electrodynamics of Plasma and Plasma-Like Media [in Russian], Gosatomizdat, Moscow (1961).

    Google Scholar 

  4. N. L. Tsintsadze, “Some new aspects of degenerate quantum plasma,” in: New Frontiers in Advanced Plasma Physics (AIP Conf. Proc., Vol. 1306, B. Eliasson and P. K. Shukla, eds.), AIP, Melville, N. Y. (2010), pp. 75–88; arXiv:1010.0073v1 [physics.plasm-ph] (2010).

    Google Scholar 

  5. Yu. L. Klimontovich and V. P. Silin, Sov. Phys. Usp., 3, 84–14 (1960).

    Article  ADS  Google Scholar 

  6. I. M. Gamba, M. P. Gualdani, and C. Sparber, Kinetic and Related Modes, 2, 181–189 (2009).

    Article  MATH  MathSciNet  Google Scholar 

  7. V. I. Tatarskii, Sov. Phys. Usp., 26, 311–327 (1983).

    Article  ADS  MathSciNet  Google Scholar 

  8. G. Manfredi, “How to model quantum plasmas,” in: Topics in Kinetic Theory (Fields Inst. Commun., Vol. 46, T. Passot, C. Sulem, and P. L. Sulem, eds.), Amer. Math. Soc., Providence, R. I. (2005), pp. 263–287; arXiv:quant-ph/0505004v1 (2005).

    Google Scholar 

  9. D. Pines, J. Nucl. Energy C, 2, 5–17 (1961).

    Article  ADS  MathSciNet  Google Scholar 

  10. A. Arnold, Transport Theory Statist. Phys., 30, 561–584 (2001).

    Article  MATH  ADS  Google Scholar 

  11. P. L. Bhatnagar, E. P. Gross, and M. Krook, Phys. Rev., 94, 511–525 (1954).

    Article  MATH  ADS  Google Scholar 

  12. E. P. Wigner, Phys. Rev., 40, 749–759 (1932).

    Article  MATH  ADS  Google Scholar 

  13. M. Hillery, R. F. O’Connell, M. O. Scully, and E. P. Wigner, Phys. Rep., 106, 121–167 (1984).

    Article  ADS  MathSciNet  Google Scholar 

  14. E. M. Lifshitz and L. P. Pitaevskii, Physical Kinetics (Vol. 10 of Course of Theoretical Physics by L. D. Landau and E. M. Lifshitz), Nauka, Moscow (1979); English transl., Butterworth-Heinemann, Oxford (1981).

    Google Scholar 

  15. P. M. Platzman and P. A. Wolf, Waves and Interactions in Solid State Plasma, Acad. Press, New York (1973).

    Google Scholar 

  16. J. Lindhard, Danske Vid. Selsk. Mat.-Fys. Medd., 28, No. 8, 1–57 (1954).

    MathSciNet  Google Scholar 

  17. K. L. Kliewer and R. Fuchs, Phys. Rev., 181, 552–558 (1969).

    Article  ADS  Google Scholar 

  18. R. Fuchs and K. L. Kliewer, Phys. Rev., 185, 905–913 (1969).

    Article  ADS  Google Scholar 

  19. R. Fuchs and K. L. Kliewer, Phys. Rev. B, 3, 2270–2278 (1971).

    Article  ADS  Google Scholar 

  20. W. Kohn and S. H. Vosko, Phys. Rev., 119, 912–918 (1960).

    Article  ADS  Google Scholar 

  21. W. Kohn and L. J. Sham, Phys. Rev., 137, A1697-A1705 (1965).

  22. W. A. Harrison, Solid State Theory, McGraw-Hill, New York (1970).

    Google Scholar 

  23. P. A. Éminov, JETP, 108, 898–904 (2009).

    Article  ADS  Google Scholar 

  24. N. D. Mermin, Phys. Rev. B, 1, 2362–2363 (1970).

    Article  ADS  Google Scholar 

  25. J. Kroha, J. Non-crystalline Solids, 250—252, 865–868 (1999); arXiv:cond-mat/9810068v1 (1998).

    Article  Google Scholar 

  26. K. P. Gurov, Foundations of the Kinetic Theory: Method of N. N. Bogoliubov [in Russian], Nauka, Moscow (1966).

    Google Scholar 

  27. M. Opher, G. J. Morales, and J. N. Leboeuf, Phys. Rev. E, 66, 016407 (2002).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. V. Latyshev.

Additional information

__________

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 169, No. 3, pp. 431–443, December, 2011.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Latyshev, A.V., Yushkanov, A.A. Longitudinal permittivity of a quantum degenerate collisional plasma. Theor Math Phys 169, 1740–1750 (2011). https://doi.org/10.1007/s11232-011-0148-1

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11232-011-0148-1

Keywords

Navigation