相关论文: Chaos, Regularity, and Noise in Self-Gravitating S…
Gravitational N-body simulations, that is numerical solutions of the equations of motions for N particles interacting gravitationally, are widely used tools in astrophysics, with applications from few body or solar system like systems all…
Using controlled numerical N-body experiments, we show how, in the collapse dynamics of an initially cold and uniform distribution of particles with a generic asymmetric shape, finite $N$ fluctuations and perturbations induced by the…
In this talk I describe recent joint works with R.Schoen and with G.Gibbons and R.Schoen which prove the non-existence of certain asymptotically flat, stationary solutions of the Einstein equations with more than one body. The basic…
We study the bar instability in collisionless, rotating, anisotropic, stellar systems, using N-body simulations and also the matrix technique for calculation of modes with the perturbed collisionless Boltzmann equation. These methods are…
These notes deal with the mean-field approximation for equilibrium states of N-body systems in classical and quantum statistical mechanics. A general strategy for the justification of effective models based on statistical independence…
We revisit the problem of the equations of motion of a system of $N$ self-interacting massive particles (without spins) in the first post-Minkowskian (1PM) approximation of general relativity. We write the equations of motion, gravitational…
In this Letter we pose the question of whether a many-body quantum system with a full set of conserved quantities can relax to an equilibrium state, and, if it can, what the properties of such state are. We confirm the relaxation hypothesis…
The stability under radial and vertical perturbations of circular orbits associated to particles orbiting a spherically symmetric center of attraction is study in the context of the n-dimensional: Newtonian theory of gravitation, Einstein's…
The goal of the present account is to review our efforts to obtain and apply a ``collective'' Hamiltonian for a few, approximately decoupled, adiabatic degrees of freedom, starting from a Hamiltonian system with more or many more degrees of…
We discuss the differences and analogies of gravitational clustering in finite and infinite systems. The process of collective, or violent, relaxation leading to the formation of quasi-stationary states is one of the distinguished features…
We review recent developments in structural stability as applied to key topics in general relativity. For a nonlinear dynamical system arising from the Einstein equations by a symmetry reduction, bifurcation theory fully characterizes the…
The effects of discreteness arising from the use of the N-body method on the accuracy of simulations of cosmological structure formation are not currently well understood. After a discussion of how the relevant discretisation parameters…
We consider the problem of constructing static, elastic, many-body systems in Einstein gravity. The solutions constructed are deformations of static many-body configurations in Newtonian gravity. No symmetry assumptions are made.
Motivated by experimental probes of general relativity, we adopt methods from perturbative (quantum) field theory to compute, up to certain integrals, the effective lagrangian for its n-body problem. Perturbation theory is performed about a…
Violent relaxation (VR) is often regarded as the mechanism leading stellar systems to collisionless meta equilibrium via rapid changes in the collective potential. We investigate the role of chaotic instabilities on single particle orbits…
A model one-dimensional self consistent steady state collisionless self-gravitating system in which all the particles have the same energy is presented. This has the remarkable property that the position and velocity of the particles…
We present a theory for the dynamical evolution of a quantum system coupled to a complex many-body intrinsic system/environment. By modelling the intrinsic many-body system with parametric random matrices, we study the types of effective…
Recently, interest has increased in the entanglement of remote quantum particles through the Newtonian gravitational interaction, both from a fundamental perspective and as a test case for the quantization of gravity. Likewise,…
The self-gravitating gas in thermal equilibrium is studied using a Newtonian potential regularized at short distances. This short distance cutoff permits us to obtain a complete description of the gas including its collapsed phase. We give…
This work investigates the geometrical properties of self-gravitating $N$-body systems from the perspective established by Henri Poincar\'e and Albert Einstein concerning the operational nature of measured geometry. Utilizing recent…