2017
Том 69
№ 9

All Issues

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

Gerasimenko V. I., Shtyk V. O.

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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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