The Schr\"odinger formulation of the Feynman path centroid density

We present an analysis of the Feynman path centroid density that provides new insight into the correspondence between the path integral and the Schr\"odinger formulations of statistical mechanics. The path centroid density is a central concept for several approximations (centroid molecular dynamics, quantum transition state theory, and pure quantum self-consistent harmonic approximation) that are used in path integral studies of thermodynamic and dynamical properties of quantum particles. The centroid density is related to the quasi-static response of the equilibrium system to an external force. The path centroid dispersion is the canonical correlation of the position operator, that measures the linear change in the mean position of a quantum particle upon the application of a constant external force. At low temperatures, this quantity provides an approximation to the excitation energy of the quantum system. In the zero temperature limit, the particle's probability density obtained by fixed centroid path integrals corresponds to the probability density of minimum energy wave packets, whose average energy define the Feynman effective classical potential.Comment: 29 pages, 2 figures, 1 Table, J. Chem. Phys. (in press

Self-Consistent Relativistic Calculation of Nucleon Mean Free Path

We present a fully self-consistent and relativistic calculation of the nucleon mean free path in nuclear matter and finite nuclei. Starting from the Bonn potential, the Dirac-Brueckner-Hartree-Fock results for nuclear matter are parametrized in terms of an effective $\sigma$-$\omega$ Lagrangian suitable for the relativistic density-dependent Hartree-Fock (RDHF) approximation. The nucleon mean free path in nuclear matter is derived from this effective Lagrangian taking diagrams up to fourth-order into account. For the nucleon mean free path in finite nuclei, we make use of the density determined by the RDHF calculation in the local density approximation. Our microscopic results are in good agreement with the empirical data and predictions by Dirac phenomenology.Comment: 16 pages RevTex and 6 figures (paper, available upon request from [email protected]) UI-NTH-931