Dynamics of One-Dimensional Bose Liquids: Andreev-Like Reflection atYJunctions and the Absence of the Aharonov-Bohm Effect

We study one-dimensional Bose liquids of interacting ultracold atoms in the $Y$-shaped potential when each branch is filled with atoms. We find that the excitation packet incident on a single $Y$ junction should experience a negative density reflection analogous to the Andreev reflection at normal-superconductor interfaces, although the present system does not contain fermions. In a ring-interferometer-type configuration, we find that the transport is completely insensitive to the (effective) flux contained in the ring, in contrast with the Aharonov-Bohm effect of a single particle in the same geometry.