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Recurrence time is evaluated for some initial quantum states in theone-dimensional Bose gas with repulsive short-range interactions. In therelatively strong and weak coupling cases some different types of initialstates show almost complete recurrence and the estimates of recurrence time areproportional to some powers of the system size at least in some range of thesystem size. They are much longer than in the case of free particles such as100 times. In the free-bosonic and free-fermionic regimes we evaluate therecurrence time rigorously, which is proportional to the square of the systemsize. The estimate of recurrence time is given by the order of ten millisecondsin the corresponding experimental systems of cold atoms trapped in onedimension of ten micrometers in length. It is much shorter than the estimate ina generic quantum many-body system, which may be as long as the age of theuniverse.

Recurrence time in the quantum dynamics of the 1D Bose gas