Relaxation processes in one-dimensional self-gravitating many-body systems

Abstract

Though one dimensional self-gravitating $N$-body systems have been studied for three decade, the nature of relaxation was still unclear. There were inconsistent results about relaxation time; some initial state relaxed in the time scale $T\sim N{t}_c$, but another state did not relax even after $T\sim N^2{t}_c$, where $t_c$ is the crossing time. The water-bag distribution was believed not to relax after $T\sim N^2{t}_c$. In our previous paper, however, we found there are two different relaxation times in the water-bag distribution;in the faster relaxation ( microscopic relaxation ) the equipartition of energy distribution is attains but the macroscopic distribution turns into the isothermal distribution in the later relaxation (macroscopic relaxation). In this paper, we investigated the properties of the two relaxation. We found that the microscopic relaxation time is $T\sim N{t}_c$, and the macroscopic relaxation time is proportional to $N{t}_c$, thus the water-bag does relax. We can see the inconsistency about the relaxation times is resolved as that we see the two different aspect of relaxations. Further, the physical mechanisms of the relaxations are presented.

11 pages, uuencoded, compressed Postscript, no figure, figures available at ftp://ferio.mtk.nao.ac.jp/pub/tsuchiya/Tsuchiya95.tar.gz

References in corpus (1)

• Quasi-equilibria in one-dimensional self-gravitating many body systems

Cited by in corpus (24)

• Negative Specific Heat in Astronomy, Physics and Chemistry
• Nonequilibrium Statistical Mechanics of Systems with Long-Range Interactions: Ubiquity of Core-Halo Distributions
• Kinetic theory of long-range interacting systems with angle-action variables and collective effects
• Schrödinger method as N-body double and UV completion of dust
• Origin of scaling structure and non-gaussian velocity distribution in self-gravitating ring model
• Quasi-stationary states in the self-gravitating sheet model
• Relaxation to thermal equilibrium in the self-gravitating sheet model
• Kinetic theory of Onsager's vortices in two-dimensional hydrodynamics
• Algebraic Correlation Function and Anomalous Diffusion in the HMF model
• Chaotic itinerancy and thermalization in one-dimensional self-gravitating systems
• Kinetic theory of two-dimensional point vortices with collective effects
• Kinetic theory of $1D$ homogeneous long-range interacting systems sourced by $1/N^2$ effects
• Linear theory and violent relaxation in long-range systems: a test case
• A one-dimensional toy model of globular clusters
• Statistical Mechanics of Relativistic One-Dimensional Self-Gravitating Systems
• Slow relaxation to equipartition in spring-chain systems
• Hierarchical clustering and formation of power-law correlation in 1-dimensional self-gravitating system
• Long-time behavior and relaxation of power-law correlation in one-dimensional self-gravitating system
• Apparent violation of equipartition of energy in constrained dynamical systems
• Simulating generalised fluids via interacting wave packets evolution
• Lyapunov Instability versus Relaxation Time in two Coupled Oscillators
• Dynamics to the universal structure of one-dimensional self-gravitating systems in the quasi-equilibrium state
• Violent relaxation in one-dimensional self-gravitating system: deviation from the Vlasov limit due to finite-$N$ effect
• Emergence of Quasi-equilibrium State and Energy Distribution for the Beads-spring Molecule Interacting with a Solvent