2019
Том 71
№ 5

All Issues

Shtyk V. O.

Articles: 1
Article (Ukrainian)

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

Gerasimenko V. I., Shtyk V. O.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2006. - 58, № 9. - pp. 1175–1191

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.