Open Multiquantum Systems. Method of a Generating Functional

Abstract

The algebraic approach to the description and representation of multiquantum (multicomponent) systems discussed in the present paper continues the approach developed in [5,9–12]. That is based on the generating multicomponent -state functional and the nonlinear completely positive map [3] functional method which extends in a natural way the variety of the processes regarded as quantum stochastic processes [2], including nonlinear ones with interaction in the system. The dynamics of such systems is considered in the Markovian approximation; the theory and classification of the corresponding “master equations” was constructed in [13]. In the nonlinear case we obtain in a natural way a nonlinear extension of the basic constructions and results of the representation theory and an extension to nonlinear structures (state and mapping) [3,81 which are good tools to describe systems with interaction.