Initial-value problem of the quantum dual BBGKY hierarchy

We present a rigorous formalism to describe the evolution of observables of quantum many-particle systems. We construct a solution of the initial-value problem of the quantum dual BBGKY hierarchy of equations as an expansion over particle clusters, whose evolution is governed by the corresponding-order cumulant (semi-invariant) of the evolution operators of finitely many particles. For initial data from the space of sequences of bounded operators the existence and uniqueness theorem is proved. PACS 05.30.-d – Quantum statistical mechanics. PACS 03.65.-w – Quantum mechanics. PACS 05.20.Dd – Kinetic theory.