  In classically chaotic systems, small differences in initial conditions are
exponentially magnified over time. However, it was observed experimentally that
the (necessarily quantum) "branched flow" pattern of electron flux from a
quantum point contact (QPC) traveling over a random background potential in
two-dimensional electron gases(2DEGs) remains substantially invariant to large
changes in initial conditions. Since such a potential is classically chaotic
and unstable to changes in initial conditions, it was conjectured that the
origin of the observed stability is purely quantum mechanical, with no
classical analog. In this paper, we show that the observed stability is a
result of the physics of the QPC and the nature of the experiment. We show that
the same stability can indeed be reproduced classically, or quantum
mechanically. In addition, we explore the stability of the branched flow with
regards to changes in the eigenmodes of quantum point contact.
