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arXiv · 1008.2100

Towards Rigorous Derivation of Quantum Kinetic Equations

V. I. Gerasimenko·Zh. A. Tsvir
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Abstract

We develop a rigorous formalism for the description of the evolution of states of quantum many-particle systems in terms of a one-particle density operator. For initial states which are specified in terms of a one-particle density operator the equivalence of the description of the evolution of quantum many-particle states by the Cauchy problem of the quantum BBGKY hierarchy and by the Cauchy problem of the generalized quantum kinetic equation together with a sequence of explicitly defined functionals of a solution of stated kinetic equation is established in the space of trace class operators. The links of the specific quantum kinetic equations with the generalized quantum kinetic equation are discussed.

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V. I. Gerasimenko, Zh. A. Tsvir. 2010-08-12. Towards Rigorous Derivation of Quantum Kinetic Equations. https://doi.org/10.1088/1751-8113%2F43%2F48%2F485203

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