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• W3103469192 startingPage "175002" @default.
• W3103469192 abstract "In this article, several aspects of the dynamics of a toy model for longrange Hamiltonian systems are tackled focusing on linearly unstable unmagnetized (i.e. force-free) cold equilibria states of the Hamiltonian Mean Field (HMF). For special cases, exact finite-N linear growth rates have been exhibited, including, in some spatially inhomogeneous case, finite-N corrections. A random matrix approach is then proposed to estimate the finite-N growth rate for some random initial states. Within the continuous, $N rightarrow infty$, approach, the growth rates are finally derived without restricting to spatially homogeneous cases. All the numerical simulations show a very good agreement with the different theoretical predictions. Then, these linear results are used to discuss the large-time nonlinear evolution. A simple criterion is proposed to measure the ability of the system to undergo a violent relaxation that transports it in the vicinity of the equilibrium state within some linear e-folding times." @default.
• W3103469192 created "2020-11-23" @default.
• W3103469192 creator A5085745718 @default.
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• W3103469192 date "2011-04-04" @default.
• W3103469192 modified "2023-09-25" @default.
• W3103469192 title "Linear theory and violent relaxation in long-range systems: a test case" @default.
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• W3103469192 doi "https://doi.org/10.1088/1751-8113/44/17/175002" @default.
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