Relaxation of quasi-stationary states in long range interacting systems and a classification of the range of pair interactions

• Authors: Bruno Marcos , Andrea Gabrielli , Michael Joyce
• Languages of publication: EN

Abstracts

EN

Systems of particles interacting with long range interactions present generically ”quasi-stationary states” (QSS), which are approximately time-independent out of equilibrium states. In this proceedings, we explore the generalization of the formation of such QSS and their relaxation from the much studied case of gravity to a generic pair interaction with the asymptotic form of the potential v(r) ∼ 1/r
γ with γ > 0 in d dimensions. We compute analytic estimations of the relaxation time calculating the rate of two body collisionality in a virialized system approximated as homogeneous. We show that for γ < (d − 1/2), the collision integral is dominated by the size of the system, while for γ > (d − 1/2), it is dominated by small impact parameters. In addition, the lifetime of QSS increases with the number of particles if γ < d − 1 (i.e. the force is not integrable) and decreases if γ > d − 1. Using numerical simulations we confirm our analytic results. A corollary of our work gives a ”dynamical” classification of interactions: the dynamical properties of the system depend on whether the pair force is integrable or not.

Keywords

EN

long range interacting systems; Vlasov equation; collisional relaxation

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2012
• Volume: 10
• Issue: 3
• Pages: 676-683

Dates

published

1 - 6 - 2012

online

17 - 6 - 2012

Contributors

author

Bruno Marcos

author

Andrea Gabrielli

author

Michael Joyce

References

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Identifiers

DOI

10.2478/s11534-012-0032-0