 02112 Paolo Butta', Emanuele Caglioti, Carlo Marchioro
 On the long time behavior of infinitely extended systems of
particles interacting via Kac potentials
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Mar 8, 02

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Abstract. We analyze the long time behavior of an infinitely extended system of
particles in one dimension, evolving according to the Newton laws and
interacting via a nonnegative superstable Kac potential $\phi_\ga(x) =
\ga\phi(\ga x)$, $\ga\in (0,1]$. We first prove that the velocity of a
particle grows at most linearly in time, with rate of order $\ga$. We
next study the motion of a fast particle interacting with a background
of slow particles, and we prove that its velocity remains almost unchanged
for a very long time (at least proportional to $\ga^{1}$ times the velocity
itself). Finally we shortly discuss the so called ``Vlasov limit'', when
time and space are scaled by a factor $\ga$.
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