Relaxation of a 1-D gravitational system

Abstract

We study the relaxation towards thermodynamical equilibrium of a 1-D gravitational system. This OSC model shows a series of critical energies $E_{cn}$ where new equilibria appear and we focus on the homogeneous ($n=0$), one-peak ($n=\pm 1$) and two-peak ($n=2$) states. Using numerical simulations we investigate the relaxation to the stable equilibrium $n=\pm 1$ of this $N-$body system starting from initial conditions defined by equilibria $n=0$ and $n=2$. We find that in a fashion similar to other long-range systems the relaxation involves a fast violent relaxation phase followed by a slow collisional phase as the system goes through a series of quasi-stationary states. Moreover, in cases where this slow second stage leads to a dynamically unstable configuration (two peaks with a high mass ratio) it is followed by a new sequence ``violent relaxation/slow collisional relaxation''. We obtain an analytical estimate of the relaxation time $t_{2\to \pm 1}$ through the mean escape time of a particle from its potential well in a bistable system. We find that the diffusion and dissipation coefficients satisfy Einstein's relation and that the relaxation time scales as $N{e}^{1/T}$ at low temperature, in agreement with numerical simulations.

15 pages, published in Phys. Rev. E

References in corpus (15)

• Stability criteria of the Vlasov equation and quasi-stationary states of the HMF model
• Dynamics and thermodynamics of a simple model similar to self-gravitating systems: the HMF model
• Prediction of anomalous diffusion and algebraic relaxations for long-range interacting systems, using classical statistical mechanics
• On the lifetime of metastable states in self-gravitating systems
• Hamiltonian and Brownian systems with long-range interactions
• The Vlasov equation and the Hamiltonian Mean-Field model
• Dynamics and Thermodynamics of Systems with Long Range Interactions: an Introduction
• The stochastic process of equilibrium fluctuations, of a system with long range interactions
• Asymptotic behavior of a stratified perturbation in a three dimensional expanding Universe
• On the dynamics of a self-gravitating medium with random and non-random initial conditions
• Dynamics and nonequilibrium states in the Hamiltonian mean-field model: A closer look
• Chaotic itinerancy and thermalization in one-dimensional self-gravitating systems
• The self-gravitating gas in the presence of dark energy
• Anomalously slow phase transitions in self-gravitating systems
• The Self-Gravitating Gas in the Presence of Dark Energy: Monte-Carlo Simulations and Stability Analysis

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