Equilibrium properties, centroid

Cao, J., Voth, G.A. The formulation of quantum statistical mechanics based on the Feynman path centroid density. I. Equilibrium properties. J. Chem. Phys. 100 (1994) 5093-5105 II Dynamical properties. J. Chem. Phys. 100 (1994) 5106-5117 III. Phase space formalism and nalysis of centroid molecular dynamics. J. Chem. Phys. 101 (1994) 6157-6167 IV. Algorithms for centroid molecular dynamics. J. Chem. Phys. 101 (1994) 6168-6183 V. Quantum instantaneous normal mode theory of liquids. J. Chem. Phys. 101 (1994) 6184 6192. 

The broad topics of this article are organized into sections as follows In Section II the centroid density-based formulation for calculating equilibrium properties in quantum mechanical systems is described. Then... 

In this article a perspective on quantum statistical mechanics and dynamics has been reviewed that is based on the path centroid variable in Feynman path integration [1,3-8,21-23]. Although significant progress has been achieved in this research effort to date, much remains to be done. For example, in terms of the calculation of equilibrium properties it... 

Cao J, Voth GA (1994a) The formulation of quantum statistical mechanics based on the feynman path centroid density, i. equilibrium properties. J Chem Phys 100 5093... 

Abstract The theoretical basis for the quantum time evolution of path integral centroid variables is described, as well as the motivation for using these variables to study condensed phase quantum dynamics. The equihbrium centroid distribution is shown to be a weU-defmed distribution function in the canoiucal 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 equilibrium 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. 

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