  In this paper we introduce and analyse Langevin samplers that consist of
perturbations of the standard underdamped Langevin dynamics. The perturbed
dynamics is such that its invariant measure is the same as that of the
unperturbed dynamics. We show that appropriate choices of the perturbations can
lead to samplers that have improved properties, at least in terms of reducing
the asymptotic variance. We present a detailed analysis of the new Langevin
sampler for Gaussian target distributions. Our theoretical results are
supported by numerical experiments with non-Gaussian target measures.
