相关论文: Kinetic theory of collisionless relaxation for sys…
We develop the kinetic theory of Hamiltonian systems with weak long-range interactions. Starting from the Klimontovich equation and using a quasilinear theory, we obtain a general kinetic equation that can be applied to spatially…
We develop a kinetic theory of systems with long-range interactions taking collective effects and spatial inhomogeneity into account. Starting from the Klimontovich equation and using a quasilinear approximation, we derive a…
The long-term dynamics of long-range interacting $N$-body systems can generically be described by the Balescu-Lenard kinetic equation. However, for ${1D}$ homogeneous systems, this collision operator exactly vanishes by symmetry. These…
We introduce a model of uncoupled pendula, which mimics the dynamical behavior of the Hamiltonian Mean Field (HMF) model. This model has become a paradigm for long-range interactions, like Coulomb or dipolar forces. As in the HMF model,…
Dynamics of many-particle systems with long-range interaction is collisionless and governed by the Vlasov equation. This dynamics is a flow of a six-dimensional incompressible liquid with uncountable integrals of motion. If the flow…
Long-range interacting systems irreversibly relax as a result of their finite number of particles, $N$. At order $1/N$, this process is described by the inhomogeneous Balescu--Lenard equation. Yet, this equation exactly vanishes in…
We complete the existing literature on the kinetic theory of systems with long-range interactions. Starting from the BBGKY hierarchy, or using projection operator technics or a quasilinear theory, a general kinetic equation can be derived…
We review and complete the existing literature on the kinetic theory of spatially homogeneous systems with long-range interactions taking collective effects into account. The evolution of the system as a whole is described by the…
Plasmas whose Coulomb-collision rates are very small may relax on shorter time scales to non-Maxwellian quasi-equilibria, which, nevertheless, have a universal form, with dependence on initial conditions retained only via an infinite set of…
We present a kinetic theory for inhomogeneous systems with weak long-range interactions. Starting from the Klimontovich equation and using a quasilinear theory, we obtain a closed kinetic equation describing the relaxation of the…
We present a theory of collisionless relaxation in systems with long-range interactions. Contrary to Lynden-Bell's theory of violent relaxation, which assumes global ergodicity and mixing, we show that quasi-stationary states (qSS) observed…
A new kinetic theory Boltzmann-like collision term including correlations is proposed. In equilibrium it yields the one-particle distribution function in the form of a generalised-Lorentzian resembling but not being identical with the…
A theoretical framework is presented which allows to quantitatively predict the final stationary state achieved by a non-neutral plasma during a process of collisionless relaxation. As a specific application, the theory is used to study…
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 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…
Kinetic equations are derived from the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy for point vortex systems in an infinite plane. As the level of approximation for the Landau equation, the collision term of the kinetic equation…
We complete the kinetic theory of inhomogeneous systems with long-range interactions initiated in previous works. We use a simpler and more physical formalism. We consider a system of particles submitted to a small external stochastic…
Finite-$N$ effects unavoidably drive the long-term evolution of long-range interacting $N$-body systems. The Balescu-Lenard kinetic equation generically describes this process sourced by ${1/N}$ effects but this kinetic operator exactly…
A statistical theory is presented which allows to calculate the stationary state achieved by a driven system after a process of collisionless relaxation. The theory is applied to study an electron beam driven by an external electric field.…
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…