Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2005-09-29
Eur. Phys. J. B, 52, 47 (2006)
Physics
Condensed Matter
Statistical Mechanics
Scientific paper
10.1140/epjb/e2006-00267-9
We present first elements of kinetic theory appropriate to the inhomogeneous phase of the HMF model. In particular, we investigate the case of strongly inhomogeneous distributions for $T\to 0$ and exhibit curious behaviour of the force auto-correlation function and friction coefficient. The temporal correlation function of the force has an oscillatory behaviour which averages to zero over a period. By contrast, the effects of friction accumulate with time and the friction coefficient does not satisfy the Einstein relation. On the contrary, it presents the peculiarity to increase linearly with time. Motivated by this result, we provide analytical solutions of a simplified kinetic equation with a time dependent friction. Analogies with self-gravitating systems and other systems with long-range interactions are also mentioned.
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