Department of Physics, Graduate School of Humanities and Sciences, Ochanomizu University, Bunkyo-ku, Tokyo, Japan.
Phys Rev Lett. 2012 Mar 16;108(11):110401. doi: 10.1103/PhysRevLett.108.110401. Epub 2012 Mar 12.
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.
通过精确的方法，我们数值求解了一维排斥短程相互作用玻色子中初始局域态的密度分布的时间演化。我们表明，具有密度凹陷的局域态是通过叠加单空穴激发来构造的。初始密度分布与弱耦合情况下暗孤子的平方幅度图重叠。我们观察到在大量粒子（如 N=1000）的情况下，局域态平衡时塌缩成平坦的分布。弛豫时间随着耦合常数的减小而增加，这表明存在非对角长程有序。我们对少量粒子（如 N=20）的情况展示了一个重现现象。
