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arXiv · 0805.1568

Ergodicity and Central Limit Theorem in Systems with Long-Range Interactions

Annibal Figueiredo·Tarcisio Marciano da Rocha Filho·Marco Antonio Amato
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Abstract

In this letter we discuss the validity of the ergodicity hypothesis in theories of violent relaxation in long-range interacting systems. We base our reasoning on the Hamiltonian Mean Field model and show that the life-time of quasi-stationary states resulting from the violent relaxation does not allow the system to reach a complete mixed state. We also discuss the applicability of a generalization of the central limit theorem. In this context, we show that no attractor exists in distribution space for the sum of velocities of a particle other than the Gaussian distribution. The long-range nature of the interaction leads in fact to a new instance of sluggish convergence to a Gaussian distribution.

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Annibal Figueiredo, Tarcisio Marciano da Rocha Filho, Marco Antonio Amato. 2008-05-12. Ergodicity and Central Limit Theorem in Systems with Long-Range Interactions. https://doi.org/10.1209/0295-5075%2F83%2F30011

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