  We study the collision dynamics of two Bose-Einstein condensates with their
dynamical wave functions modeled by a set of coupled, time-dependent
Gross-Pitaevskii equations. Beginning with an effective one-dimensional system,
we identify regimes characterized by the relationship between inter- and
intra-atomic interactions and the initial configuration of the system, akin to
the equilibrium phase diagram of two interacting Bose condensates. We consider
a dynamical setup in which two wave packets are initially at rest with a small
separation about the center of an asymmetric harmonic trap. Upon release, we
observe a rapid approach to dynamical equilibrium in the limits of very large
and very small inter-particle repulsion, characterized by periodic transmission
or reflection of the condensates as distinguishable units, whereas the
intermediate, critical regime is characterized by extended transient dynamics,
density fracturing, and dynamical mixing. We therefore have reason to believe
that non-trivial behavior may exist during the collisions of Bose-Einstein
condensates as a result of their non-linear interactions, and these effects may
be observable in a suitable laboratory environment.
