  We demonstrate that the quantum dynamics of yrast states in the
one-dimensional (1D) Bose gas gives an illustrative example to equilibration of
an isolated quantum many-body system. We first formulate the energy spectrum of
yrast states in terms of the dressed energy by applying the method of
finite-size corrections. We then review the exact time evolution of quantum
states constructed from yrast states shown by the Bethe ansatz. In time
evolution the density profile of an initially localized quantum state
constructed from yrast states collapses into a flat profile in the case of a
large particle number such as N=1000, while recurrence of the localized state
occurs in the case of a small particle number such as N=20. We suggest that the
dynamical relaxation behavior for the large N case is consistent with the
viewpoint of typicality for generic quantum states: the expectation values of
local operators valuated in most of quantum states are very close to those of
the micro-canonical ensemble.
