Using density matrices we describe the time evolution of nonequilibrium states with a set of hierarchical of quantum kinetic equations. An analogous formalism to this equation is developed via the path integral method in a holomorphic representation of density matrices and related to the Green’s function formalism.

The Journal of Chemical PhysicsNov 1, 19961 citation

Russian Physics Journal

Integral equations for particle density matrices

Dmitri M Gitman, A. E. Arinshtein

Published Aug 1, 1968• 0 citations

Publisher

DOI: 10.1007/bf01106040

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The binary collision expansion for the density matrix of a system of

N

particles with pair interaction was derived by Huang, Lee, and Yang by expansion in the interaction and subsequent summation over terms represented by certain classes of diagrams. A simpler derivation has been obtained by the use of the $\frac{N(N\ensuremath{-}1)}{2}$ integral equations which relate the density matrix of the system to the density matrices of systems in which only one pair of particles interacts. Successive substitution of the integral equations into each other yields an expansion which by a trivial additional step becomes the binary collision expansion. Our derivation shows also that the binary collision expansion is the Laplace inverse of the coordinate representation of the expansion in terms of scattering operators.