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We present a dynamical technique for sampling the canonical measure in molecular dynamics. The method controls temperature by use of a device similar to that of Nosé dynamics, but adds random noise to improve ergodicity. In contrast to Langevin dynamics, where noise is added directly to each physical degree of freedom, our method relies on an indirect coupling to a single Brownian particle. For a model with harmonic potentials, we show under a mild non-resonance assumption that the new dynamics generates the canonical distribution. In spite of its stochastic nature, it appears to have a relatively weak effect on the physical dynamics, as measured by perturbation of temporal autocorrelation functions. The kinetic energy is tightly controlled even in the early stages of a simulation.

Abstract. We present sharp convergence results for the Cauchy-Born approximation of general classical atomistic interactions, for static problems with small data and for dynamic problems on a macroscopic time interval.