Ergodicity in a two-dimensional self gravitating many body system

C. H. Silvestre; T. M. Rocha Filho

doi:10.1016/j.physleta.2015.10.042

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arXiv · 1501.00628

Ergodicity in a two-dimensional self gravitating many body system

C. H. Silvestre·T. M. Rocha Filho

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Abstract

We study the ergodic properties of a two-dimensional self-gravitating system using molecular dynamics simulations. We apply three different tests for ergodicity: a direct method comparing the time average of a particle momentum and position to the respective ensemble average, sojourn times statistics and the dynamical functional method. For comparison purposes they are also applied to a short-range interacting system and to the Hamiltonian mean-field model. Our results show that a two-dimensional self-gravitating system takes a very long time to establish ergodicity. If a Kac factor is used in the potential energy, such that the total energy is extensive, then this time is independent of particle number, and diverges with $\sqrt{N}$ without a Kac factor.

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C. H. Silvestre, T. M. Rocha Filho. 2015-10-12. Ergodicity in a two-dimensional self gravitating many body system. https://doi.org/10.1016/j.physleta.2015.10.042

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