  Recurrence time is evaluated for some initial quantum states in the
one-dimensional Bose gas with repulsive short-range interactions. In the
relatively strong and weak coupling cases some different types of initial
states show almost complete recurrence and the estimates of recurrence time are
proportional to some powers of the system size at least in some range of the
system size. They are much longer than in the case of free particles such as
100 times. In the free-bosonic and free-fermionic regimes we evaluate the
recurrence time rigorously, which is proportional to the square of the system
size. The estimate of recurrence time is given by the order of ten milliseconds
in the corresponding experimental systems of cold atoms trapped in one
dimension of ten micrometers in length. It is much shorter than the estimate in
a generic quantum many-body system, which may be as long as the age of the
universe.
