Non-equilibrium dynamics of two-dimensional infinite particle systems with a singular interaction
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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.
KeywordsParticle System Initial Configuration Continuity Property Main Condition Interparticle Distance
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- 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.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.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.Ruelle, D.: Superstable interactions in classical statistical mechanics. Commun. math. Phys.18, 127–159 (1970)Google Scholar
- 5.Ruelle, D.: Classical statistical mechanics of a system of particles. Helv. Phys. Acta36, 183–197 (1963)Google Scholar
- 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.Ruelle, D.: Statistical mechanics, rigorous results. New York-Amsterdam: Benjamin 1969Google Scholar