论文标题
量子双暗丝体的动力学和玻色 - 因斯坦冷凝的精确尺寸缩放的动力学
Dynamics of quantum double dark-solitons and an exact finite-size scaling of Bose-Einstein condensation
论文作者
论文摘要
我们在Lieb-Liniger模型中的量子双暗岩态的确切非平衡动力学中显示了一些新颖的方面，用于具有排斥性相互作用的一维玻色气体。我们还显示了基态的玻色子凝结（BEC）的确切大小的缩放尺寸，这应该表征我们假设我们假设在弱耦合方面发生的量子双重黑 - 丝岩中的准BEC。首先，我们显示了伯特·安萨兹（Bethe Ansatz）与量子双重暗仪相关的量子状态中密度曲线的确切时间演变。其次，我们通过精确评估量子双 - 丝状状态之间的磁场元素的矩阵元素的平方幅度和相位剖面，从而有效地得出了一种有效的宏观量子波功能。这些概况接近了黑暗 - 岩石的概况，尤其是在弱耦合方面。然后，精确地证明了量子双暗丝岩状态中两个缺口的散射。从上面的观察结果表明，准BEC应在量子双暗 - 苏利顿状态的动力学中起重要作用。如果冷凝物分数接近1，则量子状态应与均值范围图像有效的准BEC状态近似。
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 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.
