Initial-value problem for the Bogolyubov hierarchy for quantum systems of particles
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.
English version (Springer): Ukrainian Mathematical Journal 58 (2006), no. 9, pp 1329-1346.
Citation Example: Gerasimenko V. I., Shtyk V. O. Initial-value problem for the Bogolyubov hierarchy for quantum systems of particles // Ukr. Mat. Zh. - 2006. - 58, № 9. - pp. 1175–1191.
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