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Springer, Numerische Mathematik, 2(100), p. 211-232, 2005

DOI: 10.1007/s00211-005-0599-0

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Long-time averaging for integrable Hamiltonian dynamics

Journal article published in 2005 by Eric Cancès, Eric Canc�s, François Castella, Philippe Chartier, Erwan Faou, Claude Le Bris, Frédéric Legoll, Claude Le Bris, Gabriel Turinici ORCID
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This paper is available in a repository.

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Abstract

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.