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| We construct numerical integrators for Hamiltonian problems that may advantageously
replace the standard Verlet time-stepper within Hybrid Monte Carlo and
related simulations. Past attempts have often aimed at boosting the order of accuracy
of the integrator and/or reducing the size of its error constants; order and
error constant are relevant concepts in the limit of vanishing step-length. We propose
an alternative methodology based on the performance of the integrator when
sampling from Gaussian distributions with not necessarily small step-lengths. We
construct new splitting formulae that require two, three or four force evaluations
per time-step. Numerical experiments suggest that the
new integrators may provide an improvement on the efficiency of the standard Verlet
method, especially in problems with high dimensionality. |
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