Feynman path centroid dynamics

Department of Chemistry and Henry Eyring Center for Theoretical Chemistry, University of Utah, 

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. 

The Feynman path integral formalism in quantum mechanics has proven to be an important vehicle for studying the quantum properties of condensed matter, both conceptually and in computational studies. Various classical-like concepts may be more easily introduced and, in the case of equilibrium properties, the formalism provides apowerful computer simulation tool. 

Feynman first suggested - that the path centroid may be the most classical-like variable in an equilibrium quantum system, thus providing the basis for the formulation of a classical-like equilibrium density function. The path centroid 

Schwartz (ed.). Theoretical Methods in Condensed Phase Chemistry, 41-68. 2000 Kluwer Academic Publishers. Printed in the Netherlands. 

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