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


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.


Particle System Initial Configuration Continuity Property Main Condition Interparticle Distance 
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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

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