Abstract

n th e G lo b a l Q u a n tu m D y n a m ic s o f M u lti-L a ttic e S y s te m s w ith N o n -lin e a r C la s s ic a l E f fe c ts * The microscopic dynamics for a class of long range interacting multi-lattice quantum systems is constructed in the thermodynamical limit by means of operator algebraic concepts. By direct estimations the existence of the limiting Schrödinger dynamics is proven for a set of states, which comprises also globally non-equilibrium situations. The expectation values of the classical observ-ables in the pure phase states are shown to satisfy a set of coupled non-linear differential equations. The limiting Heisenberg dynamics is derived as a VF*-automorphism group in the partially universal von Neumann algebra which corresponds to the selected set of states; it is in general, however, not er-weakly continuous in the time parameter.