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An Ergodic Sampling Scheme for Constrained Hamiltonian Systems with Applications to Molecular Dynamics

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Abstract

This article addresses the problem of computing the Gibbs distribution of a Hamiltonian system that is subject to holonomic constraints. In doing so, we extend recent ideas of Cancès et al. (M2AN 41(2), 351–389, 2007) who could prove a Law of Large Numbers for unconstrained molecular systems with a separable Hamiltonian employing a discrete version of Hamilton’s principle. Studying ergodicity for constrained Hamiltonian systems, we specifically focus on the numerical discretization error: even if the continuous system is perfectly ergodic this property is typically not preserved by the numerical discretization. The discretization error is taken care of by means of a hybrid Monte-Carlo algorithm that allows for sampling bias-free expectation values with respect to the Gibbs measure independently of the (stable) step-size. We give a demonstration of the sampling algorithm by calculating the free energy profile of a small peptide.

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  1. Institut für Mathematik, Freie Universität Berlin, Arnimallee 6, 14195, Berlin, Germany

    Carsten Hartmann

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Hartmann, C. An Ergodic Sampling Scheme for Constrained Hamiltonian Systems with Applications to Molecular Dynamics. J Stat Phys 130, 687–711 (2008). https://doi.org/10.1007/s10955-007-9470-2

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