Nonconservative nonlinear systems. Pt. 1

This article is the first part of a review of recent developments in the description of nonconservative and nonlinear dynamical systems. Using examples like pair production and finite lifetime of quantum states we point out that quantum mechanics can give only an approximate answer due to the fact that the physical reality is neither conservativ nor linear, both properties being vital for the formulation of quantum mechanics. Nonlinear behaviour in classical dynamics is introduced by considering phase tranditions within the framework of Ginzburg-Landau. We explain how nonlinear phenomena lead to self-organization in the case of superconductivity, where spatially periodic structures, the Aprikosov flux lattice, are formed for certain values of the magnetic field. In the last section we report on reaction-diffusion equations and population dynamics which are a rich source of nonlinear dynamics. We finish with a discussion of Prigogine's dissipative structures and the recently discovered strange attractors, which are important for the transition from deterministic to stochastic behavior. The main concepts and equations are summarized in information boxes to help the unfamiliar reader. (HJ) 891 HJ/HJ 892 BRE