Heisenberg picture of quantum kinetic evolution in mean-field limit

Gerasimenko Viktor

doi:10.3934/krm.2011.4.385

Article Contents

2011, Volume 4, Issue 1: 385-399. Doi: 10.3934/krm.2011.4.385

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Heisenberg picture of quantum kinetic evolution in mean-field limit

Gerasimenko Viktor^1,

1.
Institute of Mathematics of NAS of Ukraine, 3, Tereshchenkivs'ka Str., 01601 Kyiv-4

Received: August 31, 2010

Revised: September 30, 2010

Published: February 2011

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Abstract

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. Moreover, 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.

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Mathematics Subject Classification: Primary: 35Q40; Secondary: 47d06.

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