On quantum kinetic evolution of marginal observables V.I. Gerasimenko
Institute of Mathematics of NAS of Ukraine, 3, Tereshchenkivs’ka Str., 01601, Kyiv–4, Ukraine, E–mail: gerasym@imath.kiev.ua
We develop a rigorous formalism for the description of the evolution of observables of quantum systems of particles in the mean-field scaling limit. The corresponding asymptotics of a solution of the initial-value problem of the dual quantum BBGKY hierarchy is constructed. More- over, links of the evolution of marginal observables and the evolution of quantum states described in terms of a one-particle marginal density operator are established. Such approach gives the alternative description of the kinetic evolution of quantum many-particle systems to generally accepted approach on basis of kinetic equations.
[1] Gerasimenko V.I., Ukr. Phys. J., 2009,54, No. 8–9, 834–846.
[2] Borgioli G., Gerasimenko V.I., Nuovo Cimento C, 2010,33, No. 1, 71–78.
[3] Gerasimenko V.I., Kinetic and Related Models, 2011,4, No. 1 (sub- mitted for publication).
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