Time scales of relaxation and Lyapunov instabilities in a one-dimensional gravitating sheet system
نویسنده
چکیده
The relation between relaxation, the time scale of Lyapunov instabilities, and the Kolmogorov-Sinai time in a one-dimensional gravitating sheet system is studied. Both the maximum Lyapunov exponent and the Kolmogorov-Sinai entropy decrease as proportional to N−1/5. The time scales determined by these quantities evidently differ from any type of relaxation time found in the previous investigations. The relaxation time to quasiequilibria (microscopic relaxation) is found to coincide with the inverse of the minimum positive Lyapunov exponent. The relaxation time to the final thermal equilibrium differs to the inverse of the Lyapunov exponents and the Kolmogorov-Sinai time. Typeset using REVTEX 1
منابع مشابه
Thermal Relaxation in One-Dimensional Self-Gravitating Systems
In this paper, we study the thermal relaxation in the one-dimensional self-gravitating system, or the so-called sheet model. According to the standard argument, the thermal relaxation time of the system is around Nt c , where N is the number of sheets and t c is the crossing time. It has been claimed that the system does not reach the thermal equilibrium in this thermal relaxation timescale, an...
متن کاملLong-time behavior and relaxation of power-law correlation in one-dimensional self-gravitating system
Long-time behavior of spatial power-law correlation in one-dimensional self-gravitating system is numerically investigated. It is found that the power-law structure persists even after the system is virialized. The structure gradually disappears owing to energy exchange among particles. Energy distribution is quasi-stationary after the system is virialized.
متن کاملChaotic Itinerancy and Thermalization in One-dimensional Self-gravitating Systems
This is the third paper of the series of our studies of the one-dimensional selfgravitating many-body systems. In our rst paper (Paper I), we found there are two stages in the relaxation of the water-bag to isothermal distribution, the microscopic relaxation and the macroscopic relaxation as the faster and the slower relaxation, respectively. In the second paper (Paper II), we derived the time ...
متن کاملNAO-TAP-1995-1 OU-TAP-18 DPNU-95-15 Relaxation processes in one-dimensional self-gravitating many-body systems
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 N tc, but another state did not relax even after T N 2 tc, where tc is the crossing time. The water-bag distribution was believed not to relax after T N tc. In...
متن کاملLong-term evolution of stellar self-gravitating systems away from thermal equilibrium: connection with nonextensive statistics.
With particular attention to the recently postulated introduction of a nonextensive generalization of Boltzmann-Gibbs statistics, we study the long-term stellar dynamical evolution of self-gravitating systems on time scales much longer than the two-body relaxation time. In a self-gravitating N-body system confined in an adiabatic wall, we show that the quasiequilibrium sequence arising from the...
متن کامل