Related papers: Relaxation of One-dimensional Collisionless Gravit…
We develop the kinetic theory of collisionless relaxation for systems with long-range interactions in relation to the statistical theory of Lynden-Bell. We treat the multi-level case. We make the connection between the kinetic equation…
We investigate the non-equilibrium relaxation dynamics of a one dimensional system of interacting spinless fermions near the XXZ integrable point. We observe two qualitatively different regimes: close to integrability and for low energies…
N-body simulations of collisionless collapse have offered important clues to the construction of realistic stellar dynamical models of elliptical galaxies. Such simulations confirm and quantify the qualitative expectation that rapid…
We discuss the dynamics and thermodynamics of systems with weak long-range interactions. Generically, these systems experience a violent collisionless relaxation in the Vlasov regime leading to a (usually) non-Boltzmannian quasi stationary…
The Bhatnagar-Gross-Krook (BGK) single-relaxation-time collision model for the Boltzmann equation serves as the foundation of the lattice BGK (LBGK) method developed in recent years. The description of the collision as a uniform relaxation…
We revisit the dynamics of the one-dimensional self-gravitating sheets models. We show that homogeneous and non-homogeneous states have different ergodic properties. The former is non-ergodic and the one-particle distribution function has a…
Motivated by the recent interest in non-equilibrium phenomena in quantum many-body systems, we study strongly interacting fermions on a lattice by deriving and numerically solving quantum Boltzmann equations that describe their relaxation…
Generic equilibria are derived for turbulent relaxing plasmas via an entropy-maximization procedure that accounts for the short-time conservation of certain collisionless invariants. The conservation of these collisionless invariants endows…
This paper uses dynamical invariants to describe the evolution of collisionless systems subject to time-dependent gravitational forces without resorting to maximum-entropy probabilities. We show that collisionless relaxation can be viewed…
We discuss the statistical mechanics of violent relaxation in stellar systems following the pioneering work of Lynden-Bell (1967). The solutions of the gravitational Vlasov-Poisson system develop finer and finer filaments so that a…
We study, using both theory and molecular dynamics simulations, the relaxation dynamics of a microcanonical two dimensional self-gravitating system. After a sufficiently large time, a gravitational cluster of N particles relaxes to the…
The time irreversibility and fast relaxation of collapsing $N$-body gravitating systems (as opposed to the time reversibility of the equations of motion for individual stars or particles) are traditionally attributed to information loss due…
Systems of particles with long range interactions present two important processes: first, the formation of out-of-equilibrium quasi-stationary states (QSS), and the collisional relaxation towards Maxwell-Boltzmann equilibrium in a much…
The collapse of a collisionless self-gravitating system, with the fast achievement of a quasi-stationary state, is driven by violent relaxation, with a typical particle interacting with the time-changing collective potential. It is…
We consider the evolution of an initially cold, spherically symmetric system of self-gravitating particles. At early times the system undergoes self-similar collapse of the type described by Fillmore & Goldreich and Bertschinger. This stage…
Self-gravitating systems are expected to reach a statistical equilibrium state either through collisional relaxation or violent collisionless relaxation. However, a maximum entropy state does not always exist and the system may undergo a…
Long-range interacting systems, while relaxing towards equilibrium, may get trapped in nonequilibrium quasistationary states (QSS) for a time which diverges algebraically with the system size. These intriguing non-Boltzmann states have been…
A one-dimensional Vlasov-Poisson system is considered to elucidate how the information entropies of the probability distribution functions of the electron position and velocity variables evolve in the Landau damping process. Considering the…
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 ($n=\pm 1$)…
The dynamical evolution of collisionless particles in an expanding background is described. After discussing qualitatively the key features, the gravitational clustering of collisionless particles in an expanding universe is modelled using…