Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamics and physical interpretation of quasi-stationary states in
  systems with long-range interactions   Although the Vlasov equation is used as a good approximation for a
sufficiently large $N$, Braun and Hepp have showed that the time evolution of
the one particle distribution function of a $N$ particle classical Hamiltonian
system with long range interactions satisfies the Vlasov equation in the limit
of infinite $N$. Here we rederive this result using a different approach
allowing a discussion of the role of inter-particle correlations on the system
dynamics. Otherwise for finite N collisional corrections must be introduced.
This has allowed the a quite comprehensive study of the Quasi Stationary States
(QSS) but many aspects of the physical interpretations of these states remain
unclear. In this paper a proper definition of timescale for long time evolution
is discussed and several numerical results are presented, for different values
of $N$. Previous reports indicates that the lifetimes of the QSS scale as
$N^{1.7}$ or even the system properties scales with $\exp(N)$. However,
preliminary results presented here shows indicates that time scale goes as
$N^2$ for a different type of initial condition. We also discuss how the form
of the inter-particle potential determines the convergence of the $N$-particle
dynamics to the Vlasov equation. The results are obtained in the context of
following models: the Hamiltonian Mean Field, the Self Gravitating Ring Model,
and a 2-D Systems of Gravitating Particles. We have also provided information
of the validity of the Vlasov equation for finite $N$, i. e.\ how the dynamics
converges to the mean-field (Vlasov) description as $N$ increases and how
inter-particle correlations arise.

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The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph
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The categories of this paper are: nlin