On the Initial-Value Problem to the Quantum Dual BBGKY Hierarchy

Details On the Initial-Value Problem to the Quantum Dual BBGKY Hierarchy On the Initial-Value Problem to the Quantum Dual BBGKY Hierarchy

2008-06-05

arxiv.org/abs/0806.1027v1

Nuovo Cimento Soc. Ital. Fis. C 33 (1) (2010) 71-78

Physics

Mathematical Physics

22 pages

Scientific paper

10.1393/ncc/i2010-10564-6

We develop a rigorous formalism for the description of the evolution of observables in quantum systems of particles. We construct a solution of the initial-value problem to the quantum dual BBGKY hierarchy of equations as an expansion over particle clusters whose evolution are governed by the corresponding-order dual cumulant (dual 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.

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