Dynamics of quantum double dark-solitons and an exact finite-size scaling of Bose-Einstein condensation
Dynamics of quantum double dark-solitons and an exact finite-size scaling of Bose-Einstein condensation
复制标题
量子双暗孤子动力学和玻色-爱因斯坦凝聚的精确有限尺寸缩放
DOI：
10.1088/1751-8121/acc496
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发表时间：
2023
期刊：
影响因子：
--
通讯作者：
Tetsuo Deguchi
中科院分区：
文献类型：
--
作者：
Kayo Kinjo;Jun Sato;Tetsuo Deguchi
本文研究了具有排斥作用的一维玻色气体Lieb-Liniger模型中量子双暗孤子态的精确非平衡动力学。我们还显示了一个精确的有限尺寸标度的分数准玻色-爱因斯坦凝聚（BEC）在基态，这应该表征准BEC在量子双暗孤子态，我们假设发生在弱耦合制度。首先，我们利用Bethe近似给出了量子双暗孤子量子态密度分布随时间的精确演化。其次，通过精确计算量子双暗孤子态之间的场算符矩阵元的平方振幅和相位分布，我们有效地导出了一种宏观量子波函数。特别是在弱耦合区，其轮廓接近暗孤子。在此基础上，精确地证明了量子双暗孤子态中两个凹口的散射。上述结果表明，准BEC在量子双暗孤子态的动力学中起着重要的作用。如果凝聚分数接近于1，则量子态应该很好地近似于准BEC态，其中平均场图像是有效的。
We show several novel aspects in the exact non-equilibrium dynamics of quantum double dark-soliton states in the Lieb–Liniger model for the one-dimensional Bose gas with repulsive interactions. We also show an exact finite-size scaling of the fraction of the quasi-Bose–Einstein condensation (BEC) in the ground state, which should characterize the quasi-BEC in quantum double dark-soliton states that we assume to occur in the weak coupling regime. First, we show the exact time evolution of the density profile in the quantum state associated with a quantum double dark-soliton by the Bethe ansatz. Secondly, we derive a kind of macroscopic quantum wave-function effectively by exactly evaluating the square amplitude and phase profiles of the matrix element of the field operator between the quantum double dark-soliton states. The profiles are close to those of dark-solitons particularly in the weak-coupling regime. Then, the scattering of two notches in the quantum double dark-soliton state is exactly demonstrated. It is suggested from the above observations that the quasi-BEC should play a significant role in the dynamics of quantum double dark-soliton states. If the condensate fraction is close to 1, the quantum state should be well approximated by the quasi-BEC state where the mean-field picture is valid.