论文标题
Galilean-Invariant可整合模型的速度分布的矩矩的确切结果
Exact Results for the Moments of the Rapidity Distribution in Galilean-Invariant Integrable Models
论文作者
论文摘要
我们在热力学极限中研究了一类Galilean-Invariant的一维Bethe Ansatz可溶解模型。它们的速度分布在有限间隔内服从具有差分内核的积分方程，该方程不接受封闭式解决方案。我们开发了一种一般的形式主义，使人们能够研究速度分布的时刻，表明它们满足了差异方面的方程。在Lieb-Liniger模型的情况下，明确分析了派生的方程式，并通过分析计算矩。此外，我们获得了有关弱排斥处基础能量的确切信息。获得的结果直接输入许多与物理相关的数量。
We study a class of Galilean-invariant one-dimensional Bethe ansatz solvable models in the thermodynamic limit. Their rapidity distribution obeys an integral equation with a difference kernel over a finite interval, which does not admit a closed-form solution. We develop a general formalism enabling one to study the moments of the rapidity distribution, showing that they satisfy a difference-differential equation. The derived equation is explicitly analyzed in the case of the Lieb-Liniger model and the moments are analytically calculated. In addition, we obtained the exact information about the ground-state energy at weak repulsion. The obtained results directly enter a number of physically relevant quantities.
