The reactive quantum Boltzmann equations: A derivation from an arrangement channel space representation and BBGKY hierarchy

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 equations have ‘‘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.