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It should be remarked that the diffusion mechanism of the clustered particles induced by the separatrix crossing of some of them is very fast when compared with the time scale necessary to LEP’s to escape from the potential well. As we have already said such escaping times are longer than our simulation times. However, even if the particles inside the cluster remain trapped, they can visit a phase space domain wider than the one they could visit for a fixed potential landscape
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It should be remarked that the diffusion mechanism of the clustered particles induced by the separatrix crossing of some of them is very fast when compared with the time scale necessary to LEP’s to escape from the potential well. As we have already said such escaping times are longer than our simulation times. However, even if the particles inside the cluster remain trapped, they can visit a phase space domain wider than the one they could visit for a fixed potential landscape.
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A similar scenario has been observed also for one dimensional true gravitational models in C.J. Reidl and B.N. Miller, Phys. Rev. A 46, 837 (1992)
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it has been shown that also for a one dimensional system of concentric gravitating spheres a phase trasition occurs from a more concentrated phase to a more homogeneous one. Moreover, the authors show the nonequivalence of canonical and microcanonical descriptions in proximity of the transition itself and the nonoccurrence of such transition within the grand-canonical ensemble
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Recently, in B. N. Miller and P. Youngkins, Phys. Rev. Lett. 81, 4794 (1998), it has been shown that also for a one dimensional system of concentric gravitating spheres a phase trasition occurs from a more concentrated phase to a more homogeneous one. Moreover, the authors show the nonequivalence of canonical and microcanonical descriptions in proximity of the transition itself and the nonoccurrence of such transition within the grand-canonical ensemble.
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