Towards Rigorous Derivation of Quantum Kinetic Equations

Details Towards Rigorous Derivation of Quantum Kinetic Equations Towards Rigorous Derivation of Quantum Kinetic Equations

2010-08-12

arxiv.org/abs/1008.2100v1

J. Phys. A: Math. Theor. 43 (48) (2010) 485203

Physics

Mathematical Physics

25 pages

Scientific paper

10.1088/1751-8113/43/48/485203

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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