  We study the robustness, against the leakage of bosons, of wave functions of
interacting many bosons confined in a finite box, by deriving and analyzing a
general equation of motion for the reduced density operator. We identify a
robust wave function that remains a pure state, whereas other wave functions,
such as the Bogoliubov's ground state and the ground state with a fixed number
of bosons, evolve into mixed states. Although these states all have the
off-diagonal long-range order, and almost the same energy densities, we argue
that only the robust state is realized as a macroscopic quantum state.
