This article is cited in 3 papers

Differential Equations and Mathematical Physics

Nonlinear dynamics of open quantum systems

A. Yu. Samarin

Samara State Technical University, Samara, 443100, Russian Federation

Abstract: 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, nonlocal interaction, open quantum systems, non-markovian process.

UDC: 53.03:(539.183-539.194)

MSC: 81S40, 58D30

Received: November 24, 2017
Revised: January 11, 2018
Accepted: March 12, 2018
First online: March 28, 2018

Language: English

DOI: 10.14498/vsgtu1582

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ArXiv: 1706.09405