  Beam splitters allow us to superpose two continuous single mode quantum
systems. To study the behaviour of their strongly mode mixing dynamics we
consider variable beam splitters and their dynamics using Wigner's phase space
distribution, W, the evolution of which is governed by the continuity-equation
$ \frac{\partial}{\partial \tau} W = - {\nabla } \cdot {J}$. We derive the form
of the corresponding Wigner current, J, of each outgoing mode after tracing out
the other. The influence of the modes on each other is analyzed and visualized
using their respective Wigner distributions and Wigner currents. This allows us
to perform geometrical analyses of the mode interactions, casting new light on
beam splitter behaviour. Several of the presented results should be immediately
testable in experiments.
