- 99-17 Changsoo Bahn, Yong Moon Park and Hyun Jae Yoo
- Nonequilibrium Dynamics of Infinite Particle Systems with Infinite Range
Interactions
(318K, postscript file)
Jan 17, 99
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Abstract. We discuss the existence and uniqueness of non-equilibrium dynamics of
infinitely many particles interacting via superstable pair interactions
in one and two dimensions. The interaction is allowed to be of infinite
range and of singular at the origin. Under suitable regularity conditions
on the interaction potential, we show that if the potential decreases
polynomially as the distance between interacting two particles increases,
then the tempered solution to the system of Hamiltonian equations exists.
Moreover, if the potential satisfies further that either it has
a subexponential
decreasing rate or it is everywhere two-times continuously
differentiable,
then we show that the tempered solution is unique. The results
extend those of Dobrushin
and Fritz obtained for finite range interactions.
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