Conference publications

Finite-dimensional models of nonlinear quantum mechanics

Yu.M. Aponin, E.A. Aponina

Pushchino, Moscow Region

"Математика. Компьютер. Образование". Cб. трудов X международной конференции. Под общей редакцией Г.Ю. Ризниченко Ижевск: Научно-издательский центр "Регулярная и хаотическая динамика", 2003. Vol. 2. Pp. 376-386.

Finite-dimensional models of quantum mechanics fall in to the complex dynamical systems (CDS), which behavior is determined by ordinary differential equations in a finite-dimensional complex state space. The alternative classes of nonlinear CDS, which inherit some of the features of linear quantum theory models, are introduced. The CDS with unitary nonlinearity are studied. A description is given of CDS with closed dynamical equation for density matrix. This class of systems is more extensive than the class of CDS with unitary nonlinearity.

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