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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