On time evolution for large quantum systems in superspace

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Abstract
A reformulation in a superspace is given for Van Hove and Janner’s perturbation theory based on the two‐resolvent method for nonequilibrium quantum statistical mechanics. This is attained by introducing an ordered superoperator in the superspace. As an application of our formalism, the derivation of an asymptotic generalized master equation in a Markovian form is given. Further, it is investigated how a quantum subdynamics theory similar to the Brussels school’s one can be formally constructed. Our subdynamics theory is formulated on every eigenspace of a superoperator (the ss‐Hamiltonian) of which the eigenvalue is related to the intrinsic parameter E of Van Hove and Janner’s generalized master equation.