Truncated Lévy flights and weak ergodicity breaking in the Hamiltonian mean-field model

The dynamics of the Hamiltonian mean-field model is studied in the context of continuous-time random walks. We show that the sojourn times in cells in the momentum space are well described by a one-sided truncated Lévy distribution. Consequently, the system is nonergodic for long observation times t...

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Bibliographic Details
Published in:Physical review. E, Statistical, nonlinear, and soft matter physics Statistical, nonlinear, and soft matter physics, 2014-02, Vol.89 (2), p.022106-022106, Article 022106
Main Authors: Figueiredo, A, Filho, T M Rocha, Amato, M A, Oliveira, Jr, Z T, Matsushita, R
Format: Article
Language:English
Subjects:
Algorithms
Computer Simulation
Models, Chemical
Models, Statistical
Stochastic Processes
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Summary:The dynamics of the Hamiltonian mean-field model is studied in the context of continuous-time random walks. We show that the sojourn times in cells in the momentum space are well described by a one-sided truncated Lévy distribution. Consequently, the system is nonergodic for long observation times that diverge with the number of particles. Ergodicity is attained only after very long times both at thermodynamic equilibrium and at quasistationary out-of-equilibrium states.
ISSN:1539-3755
1550-2376
DOI:10.1103/PhysRevE.89.022106