Ukrainian Mathematical Journal

, Volume 58, Issue 9, pp 1329–1346 | Cite as

Initial-value problem for the Bogolyubov hierarchy for quantum systems of particles

  • V. I. Herasymenko
  • V. O. Shtyk


We construct cumulant (semi-invariant) representations for a solution of the initial-value problem for the Bogolyubov hierarchy for quantum systems of particles. In the space of sequences of trace-class operators, we prove a theorem on the existence and uniqueness of a solution. We study the equivalence problem for various representations of a solution in the case of the Maxwell-Boltzmann statistics.


Quantum System Recurrence Relation Evolution Operator Cluster Expansion BBGKY Hierarchy 
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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • V. I. Herasymenko
    • 1
  • V. O. Shtyk
    • 1
  1. 1.Institute of MathematicsUkrainian National Academy of SciencesKyiv

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