Abstract
Systems with finite degrees of freedom and with long-range interaction are frequently trapped at quasi-stationary states before relaxing to thermal equilibrium. Short-time relaxation to quasi-stationary states is approximated by the Vlasov equation, and a statistical theory based on the Vlasov description is introduced and applied to the Hamiltonian mean-field model. The theory predicts a one-body distribution for a quasi-stationary state from a given waterbag initial distribution, and a critical curve is described on a two-dimensional parameter plane which represents a family of waterbag initial distributions. The critical curve divides the parameter plane into magnetized and non-magnetized phases of quasi-stationary states. The theoretical prediction is checked by comparing with a numerically obtained critical curve for systems with finite degrees of freedom.
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Yamaguchi, Y.Y. (2010). Out-of-Equilibrium Statistical Mechanics in a Hamiltonian System with Mean-Field Interaction. In: Haubold, H., Mathai, A. (eds) Proceedings of the Third UN/ESA/NASA Workshop on the International Heliophysical Year 2007 and Basic Space Science. Astrophysics and Space Science Proceedings. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03325-4_4
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DOI: https://doi.org/10.1007/978-3-642-03325-4_4
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