Long-time averaging for integrable Hamiltonian dynamics
Résumé
Given a Hamiltonian dynamics, we address the question of computing the space-average (referred as the ensemble average in the field of molecular simulation) of an observable through the limit of its time-average. For a completely integrable system, it is known that ergodicity can be characterized by a diophantine condition on its frequencies and that the two averages then coincide. In this paper, we show that we can improve the rate of convergence upon using a filter function in the time-averages. We then show that this convergence persists when a numerical symplectic scheme is applied to the system, up to the order of the integrator.
Domaines
Analyse numérique [math.NA]| Origine | Fichiers produits par l'(les) auteur(s) |
|---|
Loading...