The reactive quantum Boltzmann equations: A derivation from an arrangement channel space representation and BBGKY hierarchy
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Ames National Laboratory is a government-owned, contractor-operated national laboratory of the U.S. Department of Energy (DOE), operated by and located on the campus of Iowa State University in Ames, Iowa.
For more than 70 years, the Ames National Laboratory has successfully partnered with Iowa State University, and is unique among the 17 DOE laboratories in that it is physically located on the campus of a major research university. Many of the scientists and administrators at the Laboratory also hold faculty positions at the University and the Laboratory has access to both undergraduate and graduate student talent.
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Abstract
A rigorous derivation of the reactive quantum Boltzmann equations is presented for systems where breakup and recombination are excluded. The use of an arrangement channel space representation allows an exact decomposition of the N particle density matrix into components for different chemical compositions and an exact definition of reduced species density matrices (as opposed, e.g., to standard projection operator techniques). This necessitates the use of the combinatorially complex arrangement channel BBGKY hierarchy which, however, avoids the need for the usual heuristic specification of collision terms. Another advantage is that scattering equations generated for the reactive and nonreactive many body T matrices appearing in the Boltzmann equationshave ‘‘well‐behaved’’ kernels (unlike the corresponding Lippmann–Schwinger equations). From the derived equations we readily obtain, e.g., reaction‐diffusion equations and nonequilibrium expressions for the chemical reaction rates.
Comments
This article is published as Evans, J. W., D. K. Hoffman, and D. J. Kouri. "The reactive quantum Boltzmann equations: A derivation from an arrangement channel space representation and BBGKY hierarchy." The Journal of Chemical Physics 78, no. 5 (1983): 2665-2681, doi:10.1063/1.445026. Posted with permission.