Russian Physics Journal

, Volume 42, Issue 6, pp 546–551 | Cite as

Lorentz gas interacting with an inhomogeneous thermostat

  • A. P. Kasatkin
  • A. A. Yankina
Physics of Semiconductors and Dielectrics
  • 17 Downloads

Abstract

The equilibrium distribution of a Lorentz gas (“electrons”) interacting with an inhomogenous thermostat (“atoms”) is examined with consideration of 1) the concept of volumes available and forbidden for the gas particles and 2) the solution of the kinetic equation. Analytical calculations for “electrons” and “atoms” repelling each other with the force ≈r−5 (where r is the distance between the particles) have shown that the coordinate- and velocity-dependent variables in the distribution function cannot be separated. In particular, this leads to the dependence of the average kinetic energy per “electron” on the coordinate: it is higher in the region with higher density of the “atoms”. It is assumed that the Gibbs distribution does not describe the properties of the system under consideration, because in this case the interaction between the system and thermostat cannot be considered small.

Keywords

Kinetic Equation Impact Parameter Electron Velocity Gibbs Distribution Average Kinetic Energy 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    L. D. Landau and E. M. Lifshits, Statistical Physics [in Russian], Nauka, Moscow (1964).Google Scholar
  2. 2.
    A. I. Ansel'm, Principles of Statistical Physics and Thermodynamics [Russian translation], Nauka, Moscow (1973).Google Scholar
  3. 3.
    J. Uhlenbeck and J. Ford, Lectures on Statistical Mechanics [Russian translation], Mir, Moscow (1965).Google Scholar
  4. 4.
    C. Chapman and T. Couling, Mathematical Theory of Nonuniform Gases [Russian translation], GITTL, Moscow (1960).MATHGoogle Scholar
  5. 5.
    L. Boltzmann, Lectures on Gas Theory [Russian translation], GITTL, Moscow (1953).Google Scholar
  6. 6.
    Yu. L. Klimontovich, Kinetic Theory of Nonideal Gas and Nonideal Plasma [in Russian], Nauka, Moscow (1975).Google Scholar
  7. 7.
    A. P. Kasatkin and A. A. Yankina, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 5, 94 (1996).Google Scholar
  8. 8.
    G. A. Lorentz, Theory of Electrons [Russian translation], GITTL, Moscow, (1953).MATHGoogle Scholar
  9. 9.
    I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Sums, Series, and Products [in Russian], Nauka, Moscow (1971).Google Scholar
  10. 10.
    A. P. Kasatkin and V. L. Kon'kov, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 4, 95 (1980).Google Scholar
  11. 11.
    A. P. Kasatkin and V. L. Kon'kov, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 1, 103 (1982).Google Scholar

Copyright information

© Kluwer Academic/Plenum Publishers 1999

Authors and Affiliations

  • A. P. Kasatkin
  • A. A. Yankina

There are no affiliations available

Personalised recommendations