Growth of correlations in gravitational N-body simulations

Abstract

In the gravitational evolution of a cold infinite particle distribution, two-body interactions can be predominant at early times: we show that, by treating the simple case of a Poisson particle distribution in a static universe as an ensemble of isolated two-body systems, one may capture the origin of the first non-linear correlated structures. The developed power-law like behavior of the two-point correlation function is then simply related to the functional form of the time evolved nearest-neighbor probability distribution, whose time dependence can be computed by using Liouville theorem for the gravitational two-body problem. We then show that a similar dynamical evolution is also found in a large-scale ordered distribution, which has striking similarities to the case of a cosmological CDM simulation which we also consider.

arXiv comment15 pages, 28 figures

References in corpus (15)

• Nonlinear evolution of cosmological power spectra
• Evolution of structure in cold dark matter universes
• The Glass-like Universe: Real-space correlation properties of standard cosmological models
• Two body relaxation in CDM simulations
• Fundamental Discreteness Limitations of Cosmological N-Body Clustering Simulations
• Generation of Primordial Cosmological Perturbations from Statistical Mechanical Models
• Two-Body Relaxation in Cosmological Simulations
• A Test of the Particle Paradigm in N-Body Simulations
• Power-law correlation and discreteness in cosmological N-body simulations
• On the problem of initial conditions in cosmological N-body simulations
• Clustering in N-Body gravitating systems
• Comment on ''On the problem of initial conditions in cosmological N-body simulations'' (Europhys. Lett. 57, 322)
• Universality of power law correlations in gravitational clustering
• Reply to the comment on ''On the problem of initial conditions in cosmological N-body simulations''
• A cellular automaton model of gravitational clustering

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• Fractal Approach to Large-Scale Galaxy Distribution
• Gravitational dynamics of an infinite shuffled lattice: early time evolution and universality of non-linear correlations
• Statistical physics for cosmic structures
• Gravitational Structure Formation, the Cosmological Problem and Statistical Physics