Communications in Mathematical Physics

, Volume 104, Issue 3, pp 423–443 | Cite as

One-dimensional classical massive particle in the ideal gas

  • Ya. G. Sinai
  • M. R. Soloveichik


The motion of a one-dimensional massive particle under the action of collisions with points of the ideal gas is considered. It is shown that the normed displacement of the massive particle is represented asymptotically as the difference of random variables having limit Gauss distribution. Estimations of the diffusion coefficient not depending on the mass are found.


Neural Network Statistical Physic Diffusion Coefficient Complex System Nonlinear Dynamics 
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  1. 1.
    Alder, B.J., Alley, W.E.: Generalized hydrodynamics. Physics Today, January, pp. 56–63 (1984)Google Scholar
  2. 2.
    Alder, B.J., Wainwright, T.E.: Velocity autocorrelation function for hard spheres in 2 and 3 dimensions. Phys. Rev. A1, 8–20 (1970)Google Scholar
  3. 3.
    Cornfield, I.P., Fomin, S.V., Sinai, Ya.G.: Ergodic theory. Berlin, Heidelberg, New York: Springer 1982Google Scholar
  4. 4.
    Doob, J.L.: Stochastic proocesses. New York: Wiley 1953Google Scholar
  5. 5.
    Fedele, P.D., Kim, Y.W.: Direct measurement of the velocity autocorrelation function for a Brownian test particle. Phys. Rev. Lett.44, 691–694 (1980); Evidence for failure of Millikan's law of particle fall in gases. Phys. Rev. Lett.48, 403–4–6 (1982)Google Scholar
  6. 6.
    Gihman, I.I., Skorohod, A.V.: Theory of random processes. Vols. I–III. Moscow: Nauka 1971Google Scholar
  7. 7.
    Harris, T.E.: J. Appl. Prob.2, 323 (1965)Google Scholar
  8. 8.
    Major, P., Szasz, D.: On the effect of collisions on the motion of an atom inR 1. Ann. Probab.8, 1068–1078 (1980)Google Scholar
  9. 9.
    Sinai, Ya.G.: Construction of dynamics in one-dimensional systems of statistical mechanics. Theor. Math. Phys.11, 248–258 (1972)Google Scholar
  10. 10.
    Szasz, D., Toth, B.: Bounds for the limiting variance of the “Heavy Particle” inR 1. Commun. Math. Phys.104, 445–455 (1986)Google Scholar
  11. 11.
    Wiener, N.: Differential space. J. Math. Phys.2, 131–174 (1923)Google Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Ya. G. Sinai
    • 1
  • M. R. Soloveichik
    • 1
  1. 1.L. D. Landau Institute of Theoretical PhysicsAcademy of Sciences of the USSRMoscowUSSR

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