Centroid molecular dynamics defined

Abstract The theoretical basis for the quantum time evolution of path integral centroid variables is described, as weU as the motivation for using these variables to study condensed phase quantum dynamics. The equihbrium centroid distribution is shown to be a well-defined distribution function in the canonical ensemble. A quantum mechanical quasi-density operator (QDO) can then be associated with each value of the distribution so that, upon the application of rigorous quantum mechanics, it can be used to provide an exact definition of both static and dynamical centroid variables. Various properties of the dynamical centroid variables can thus be defined and explored. Importantly, this perspective shows that the centroid constraint on the imaginary time paths introduces a non-stationarity in the equihbrium ensemble. This, in turn, can be proven to yield information on the correlations of spontaneous dynamical fluctuations. This exact formalism also leads to a derivation of Centroid Molecular Dynamics, as well as the basis for systematic improvements of that theory. 

In a path-integral Monte Carlo (PIMC) calculation, the centroid force can readily be calculated from Eq. (3.64) by using the importance sampling function exp[-5p(q,. . . , qp) h] and pairwise MC moves to enforce the centroid constraint. For a path-integral molecular dynamics (PIMD) calculation [71], one defines fictitious momenta p, for each of the quasiparticles q and then runs an MD simulation with Hamilton s... 

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