Geodesic
Nonlinear dynamics of open quantum systems
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 22 (2018) no. 2, pp. 214-224

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The evolution of a composite closed system using the integral wave equation with the kernel in the form of path integral is considered. It is supposed that a quantum particle is a subsystem of this system. The evolution of the reduced density matrix of the subsystem is described on the basis of the integral wave equation for a composite closed system. The equation for the density matrix for such a system is derived. This equation is nonlinear and depends on the history of the processes in the closed system. It is shown that, in general, the reduced density matrix trace does not conserve in the evolution processes progressing in open systems and the procedure of the trace normalization is necessary as the mathematical image of a real nonlocal physical process. The wave function collapse and EPR correlation are described using this approach.
Keywords: nonlinear evolution, EPR correlation, open quantum systems
Mots-clés : nonlocal interaction, non-markovian process. 
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     author = {A. Yu. Samarin},
     title = {Nonlinear dynamics of open quantum systems},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
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     volume = {22},
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     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2018_22_2_a1/}
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A. Yu. Samarin. Nonlinear dynamics of open quantum systems. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 22 (2018) no. 2, pp. 214-224. http://geodesic.mathdoc.fr/item/VSGTU_2018_22_2_a1/