Advertisement

Communications in Mathematical Physics

, Volume 57, Issue 1, pp 67–81 | Cite as

Non-equilibrium dynamics of two-dimensional infinite particle systems with a singular interaction

  • J. Fritz
  • R. L. Dobrushin
Article

Abstract

The infinite system of Newton's equations of motion is considered for two-dimensional classical particles interacting by conservative two-body forces of finite range. Existence and uniqueness of solutions is proved for initial configurations with a logarithmic order of energy fluctuation at infinity. The semigroup of motion is also constructed and its continuity properties are discussed. The repulsive nature of interparticle forces is essentially exploited; the main condition on the interaction potential is that it is either positive or has a singularity at zero interparticle distance, which is as strong as that of an inverse fourth power.

Keywords

Particle System Initial Configuration Continuity Property Main Condition Interparticle Distance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Lanford, O.E. III.: The classical mechanics of one-dimensional systems of infinitely many particles. Commun. math. Phys.9, 169–191 (1968)Google Scholar
  2. 2.
    Lanford, O.E. III.: Time evolution of large classical systems. In: Dynamical systems, theory, and applications. Lecture notes in physics, Vol. 38, pp. 1–111. Berlin-Heidelberg-New York: Springer 1975Google Scholar
  3. 3.
    Dobrushin, R.L., Fritz, J.: Non-equilibrium dynamics of one-dimensional infinite particle systems with a hard-core interaction. Commun. math. Phys.55, 275–292 (1977)Google Scholar
  4. 4.
    Ruelle, D.: Superstable interactions in classical statistical mechanics. Commun. math. Phys.18, 127–159 (1970)Google Scholar
  5. 5.
    Ruelle, D.: Classical statistical mechanics of a system of particles. Helv. Phys. Acta36, 183–197 (1963)Google Scholar
  6. 6.
    Dobrushin, R.L.: Conditions on the asymptotic existence of the configuration integral for Gibbs distributions. (In Russian) Teor. Ver. Prim.9, 626–643 (1964)Google Scholar
  7. 7.
    Ruelle, D.: Statistical mechanics, rigorous results. New York-Amsterdam: Benjamin 1969Google Scholar

Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • J. Fritz
    • 1
  • R. L. Dobrushin
    • 2
  1. 1.Mathematical InstituteBudapestHungary
  2. 2.Institute for Problems of Information TransmissionMoscowUSSR

Personalised recommendations