论文标题
Lieb-Liniger模型的非平衡稳态：时间的多综合表示多体波功能
Non-Equilibrium Steady State of the Lieb-Liniger model: multiple-integral representation of the time evolved many-body wave-function
论文作者
论文摘要
我们继续研究非平衡稳态在量子整合模型中的出现，该模型着重于lieb-liniger气体的扩展，以进行任意排斥相互作用。作为在热力学和大距离和时间限制中可观察到的渐近物衍生的第一步，我们得出了时间演变为多体波功能的精确多个积分表示。从已知但复杂的表达开始，即几何淬灭初始状态的重叠，这些淬灭的初始状态源自伯特状态的标量产品的Slavnov公式，我们消除了对系统大小的尴尬依赖性，并将Bethe状态区分为方便的扇形。这些步骤使我们能够以各种替代形式的多重速度表达对伯特国家的不切实际的总和。此外，我们检查了所获得的集成的奇异性，并计算了多变量运动杆的贡献，这是衍生渐近造物感兴趣的必不可少的信息。
We continue our study of the emergence of Non-Equilibrium Steady States in quantum integrable models focusing on the expansion of a Lieb-Liniger gas for arbitrary repulsive interaction. As a first step towards the derivation of the asymptotics of observables in the thermodynamic and large distance and time limit, we derive an exact multiple integral representation of the time evolved many-body wave-function. Starting from the known but complicated expression for the overlaps of the initial state of a geometric quench, which are derived from the Slavnov formula for scalar products of Bethe states, we eliminate the awkward dependence on the system size and distinguish the Bethe states into convenient sectors. These steps allow us to express the rather impractical sum over Bethe states as a multiple rapidity integral in various alternative forms. Moreover, we examine the singularities of the obtained integrand and calculate the contribution of the multivariable kinematical poles, which is essential information for the derivation of the asymptotics of interest.
