Nonlinear dynamics of open quantum systems

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.

Quantum evolution as a usual mechanical motion of peculiar continua

“…2 This does not mean that there is no interaction between the material points at all. In the paper [6], the normalizing procedure required to describe the non-unitary process is considered as a mathematical image of a real physical process. Such a process is impossible without a peculiar interaction between material points.…”

“…Quantum evolution as a usual mechanical motion of peculiar continua (the third property); -any change in the measure of one of the material points subset in a local volume of space, instantly changes the measures of all the rest of other subsets in the whole space, which physically means that any local external effect on the quantum object result in the simultaneous transformation of the state of the entire continuous medium everywhere (this property have been considered in detail in [6]). To introduce the spatial distribution of the physical continuum, define the measure of the material point set occupying an infinitesimal volume as = ,…”

“…According to the paper [6] the measurement process consists of two stages. On the first of them, the quantum object interacts with the active elements of the apparatus.…”

“…Let the system consisting of the object and one of the active element be closed (such a consideration is possible if the interaction energies of the active elements each others anothers are negligible compared with their interaction energies with the object). Then the interaction of the object with the active element must obey the equation (6). This equation will be used to determine the dependence of the energy transfer rate from the object to the active particle on the complex density.…”

“…The completion stage of the measurement process is the macroscopic registering process [6], which is initiated when the energy one of the active particles increases up to a threshold value.The values of the initiation threshold for the different active particles have a statistical straggling (as well as the sensitivity ). Macroscopic changes are initiated by only one active particle, for which the threshold is exceeded before the others.…”