Departing from classical concepts of ergodic theory, formulated in terms of
probability densities, measures describing the chaotic behavior and the loss of
information in quantum open systems are proposed. As application we discuss the
chaotic outcomes of continuous measurement processes in the EEQT framework.
Simultaneous measurement of four noncommuting spin components is shown to lead
to a chaotic jump on quantum spin sphere and to generate specific fractal
images - nonlinear ifs (iterated function system). The model is purely
theoretical at this stage, and experimental confirmation of the chaotic
behavior of measuring instruments during simultaneous continuous measurement of
several noncommuting quantum observables would constitute a quantitative
verification of Event Enhanced Quantum Theory.Comment: Latex format, 20 pages, 6 figures in jpg format. New replacement has
two more references (including one to a paper by G. Casati et al on quantum
fractal eigenstates), adds example and comments concerning mixing properties
of of a two-level atom driven by a laser field, and also adds a number of
other remarks which should make it easier to follow mathematical argument
