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Ergodic properties of the multidimensional rayleigh gas with a semipermeable barrier

Journal of Statistical Physics volume 59, pages 1589–1602 (1990)Cite this article

Abstract

We consider a multidimensional system consisting of a particle of massM and radiusr (molecule), surrounded by an infinite ideal gas of point particles of massm (atoms). The molecule is confined to the unit ball and interacts with its boundary (barrier) via elastic collision, while the atoms are not affected by the boundary. We obtain convergence to equilibrium for the molecule from almost every initial distribution on its position and velocity. Furthermore, we prove that the infinite composite system of the molecule and the atoms is Bernoulli.

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References

  1. C. Boldrighini, A. Pellegrinotti, E. Presutti, Ya. G. Sinai, and M. R. Soloveychik, Ergodic properties of a semi-infinite one-dimensional system of statistical mechanics,Commun. Math. Phys. 101:363–382 (1985).

    ADS  Article  Google Scholar 

  2. I. P. Cornfeld, S. V. Fomin, and Ya. G. Sinai,Ergodic Theory (Springer-Verlag, 1982).

  3. S. Goldstein, J. L. Lebowitz, and K. Ravishankar, Ergodic properties of a system in contact with a heat bath: A one dimensional model,Commun. Math. Phys. 85:419–427 (1982).

    MathSciNet  ADS  MATH  Article  Google Scholar 

  4. M. R. Soloveychik, Ergodic properties of a system of statistical mechanics with an external potential,Izv. Akad. Nauk SSSR Ser. Mat. 53(1):179–199 (1989) [in Russian].

    Google Scholar 

  5. D. Szász and B. Tóth, Towards a unified dynamical theory of the Brownian particle in an ideal gas,Commun. Math. Phys. 111:41–62 (1987).

    ADS  MATH  Article  Google Scholar 

  6. D. Szász and B. Tóth, A dynamical theory of Brownian motion for the Rayleigh gas,J. Stat. Phys. 47:681–693 (1987).

    ADS  MATH  Article  Google Scholar 

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Authors and Affiliations

  1. Eötvös Loránd University, H-1088, Budapest, Hungary

    L. Erdős

  2. Mathematical Institute of the Hungarian Academy of Sciences, H-1364, Budapest, Hungary

    D. Q. Tuyen

Authors
  1. L. Erdős
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  2. D. Q. Tuyen
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Erdős, L., Tuyen, D.Q. Ergodic properties of the multidimensional rayleigh gas with a semipermeable barrier. J Stat Phys 59, 1589–1602 (1990). https://doi.org/10.1007/BF01334766

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  • DOI: https://doi.org/10.1007/BF01334766

Key words

  • Rayleigh gas
  • Bernoulli flow
  • Harris chain