title: Exact relaxation dynamics of a localized many-body state in the 1D Bose gas.
abstract: 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.
authors.affiliation: Department of Physics, Graduate School of Humanities and Sciences, Ochanomizu University, Bunkyo-ku, Tokyo, Japan.
authors.forename: Jun
authors.initials: J
authors.lastname: Sato
authors.forename: Rina
authors.initials: R
authors.lastname: Kanamoto
authors.forename: Eriko
authors.initials: E
authors.lastname: Kaminishi
authors.forename: Tetsuo
authors.initials: T
authors.lastname: Deguchi