Abstract
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.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 9, pp. 1175–1191, September, 2006.
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Herasymenko, V.I., Shtyk, V.O. Initial-value problem for the Bogolyubov hierarchy for quantum systems of particles. Ukr Math J 58, 1329–1346 (2006). https://doi.org/10.1007/s11253-006-0136-z
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DOI: https://doi.org/10.1007/s11253-006-0136-z