Time evolution and invariance of boson systems given by beam splittings

Based on a model for general beam splittings we search for states of boson systems which are invariant under the combination of the evolution given by the splitting procedure and some inherent evolution. It turns out that for finite systems only trivial invariant normal states may appear. However, f or locally normal states on a related quasilocal algebra representing state s of infinite boson systems, one can find examples of nontrivial invariant states. We consider as example a beam splitting combined with a contraction compensating the loss of intensity caused by the splitting process. In gen eral, we observe interesting connections between the splitting procedure an d certain thinning operations in classical probability theory. Several appl ications to physics seem to be natural since these beam splitting models ar e used to describe measuring procedures on electromagentic fields.