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Colouring the Noise

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Molecular dynamics is based on the numerical solution of Newton’s equation of motions and has provided a very powerful tool for studying complex problems in material science, physical chemistry, and biology. From the statistical mechanics point of view and under the assumption of ergodicity the temporal averages can be related to averages performed in a microcanonical ensemble in which the volume is and the number of particles are kept constant.

Real life experiments are conducted at constant pressure and temperature. It is therefore advantageous to be able to work under similar condition. We show how this is possible and in particular we shall focus on ways of controlling tha temperature of the system thus sampling is it possible to sample the Boltzmann distribution. We extend current sampling methods by using rather than straight Newton’s equations a generalized form of Langevin’s equations in which the noise is correlated (colored) rather then being white. After reviewing the theory that is behind our approach, we show how one can model the noise to achieve optimal sampling . Most remarkably our sampling method can be used to introduce quantum effect at zero additional cost with respect to a standard simulation.

This talk is part of the Scott Lectures series.

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