Exact relaxation dynamics of a localized many-body state in the 1D bose   gas
  Through an exact method we numerically solve the time evolution of the density profile for an initially localized state in the one-dimensional bosons with repulsive short-range interactions. We show that a localized state with a density notch is constructed by superposing one-hole excitations. The initial density profile overlaps the plot of the squared amplitude of a dark soliton in the weak coupling regime. We observe the localized state collapsing into a flat profile in equilibrium for a large number of particles such as N=1000. The relaxation time increases as the coupling constant decreases, which suggests the existence of off-diagonal long-range order. We show a recurrence phenomenon for a small number of particles such as N=20. 
Jun Sato, Rina Kanamoto, Eriko Kaminishi, Tetsuo Deguchi
cond-mat.quant-gas cond-mat.stat-mech